Abstract
Identify the key drivers of brand equity for Galeries Lafayette based on a questionnaire mailed to 5000 customers and returned by 600 of themThis analysis was prepared by Francisco Arrieta and Jonathan Edwards.
# options(scipen=999) #prevent scientific notation
# options(scipen=-999) #encourage scientific notation
options(scipen=0) #encourage scientific notation neutral?# kable table layout options
# do not display NAs and only 2 digits
opts <- options(knitr.kable.NA = '') #knitr.table.format = "latex"
# define table styling options
stable <- function(data, digits = 2) {
knitr::kable(data, digits=digits) |>
# kable_styling(c("striped", "condensed"))
kable_paper(full_width = F)
}# modelling
library(psych) #factor analysis tools (PAF PAF)
library(lavaan) #causal analysis
library(lm.beta) # add standarized regression coeffs
# stats
library(nortest) #Kolmogorov-Smirnov-Test
library(corrplot) #correlation matrix plot
library(olsrr) #VIF and Tolerance Values
library(pastecs) # provides function stat.desc
library(REdaS) #Bartelett's Test
# plotting & formatting
library(ggplot2) #better graphs
library(patchwork) # provides wrap_plots for multiplotting
# library(gridExtra) #provides multiplotting functionality
# library(ggpubr) #provides ggarrange for multiplotting (patchwork better though)
library(semPlot) #for visualization of path diagrams (SEM)
library(lavaanPlot) #for visualization of path diagrams (SEM)
# library(rcompanion) #Histogram and Normal Curve
library(kableExtra) #makes nice tables
# generic
library(dplyr) #useful data manip functions like arrange, distinct, rename etc included in fpp3
library(stringr) # provides string manip functions like str_split_fixed
library(Hmisc) #describe function that describes features of dataframes
library(data.table) # creating and manipulating datatables
library(knitr) #rmarkdown tools not sure why useful
library(parameters) #get model outputs in table form (good for making tabs)survey <- read.csv("Case Study III_Structural Equation Modeling.csv")
labels <- read.csv("Variables and Labels_Galeries Lafayette.csv")
dim(survey)## [1] 553 45
# head(labels)#Make labels more readable
#create copy of label column without variable code
labels["Category"] <- sub("[^-]*\\s-","",labels[["Label"]])
# labels["Category"] <- sub(".*\\s-","",labels[["Label"]])
# labels
#split this new column (category) into category and short label
labels[c("Category","Label_short")] <- str_split_fixed(labels[["Category"]],"\\?\\s\\s|\\s-", n=2)
# labels[20:25,c("Category","Label_short")]
labels[,c("Variable","Category","Label_short")] |>
stable()| Variable | Category | Label_short |
|---|---|---|
| Im1 | What do GLB represent from your point of view | Large Assortment |
| Im2 | What do GLB represent from your point of view | Assortment Variety |
| Im3 | What do GLB represent from your point of view | Artistic Decoration of Sales Area |
| Im4 | What do GLB represent from your point of view | Creative Decoration of Sales Area |
| Im5 | What do GLB represent from your point of view | Appealing Arrangement of Shop Windows |
| Im6 | What do GLB represent from your point of view | France |
| Im7 | What do GLB represent from your point of view | French Savoir-vivre |
| Im8 | What do GLB represent from your point of view | Expertise in French Traditional Cuisine |
| Im9 | What do GLB represent from your point of view | French Fashion |
| Im10 | What do GLB represent from your point of view | Gourmet Food |
| Im11 | What do GLB represent from your point of view | High-quality Cosmetics |
| Im12 | What do GLB represent from your point of view | Luxury brands |
| Im13 | What do GLB represent from your point of view | Up tp date Designer Brands |
| Im14 | What do GLB represent from your point of view | Gourmet specialities |
| Im15 | What do GLB represent from your point of view | Professional Selection of Brands |
| Im16 | What do GLB represent from your point of view | Professional Appearance Towards Customers |
| Im17 | What do GLB represent from your point of view | Are Trendy |
| Im18 | What do GLB represent from your point of view | Are Hip |
| Im19 | What do GLB represent from your point of view | Professional Organization |
| Im20 | What do GLB represent from your point of view | Relaxing Shopping |
| Im21 | What do GLB represent from your point of view | A Great Place to Stroll |
| Im22 | What do GLB represent from your point of view | Intimate Shop Atmosphere |
| C_CR1 | CO-CREATION | I would like to participate in an expert-workshop to improve the assortment of Galeries Lafayette Berlin. |
| C_CR2 | CO-CREATION | I would be available to take part in another survey at Galeries Lafayette Berlin. |
| C_CR3 | CO-CREATION | I would like to become a member of a customer group whose opinion is obtained for new products and major changes. |
| C_CR4 | CO-CREATION | I would like to participate in planning and designing special events (e.g. fashion show, introduction of new car models) if asked. |
| C_REP1 | REPURCHASE | I will continue to be a loyal customer of Galeries Lafayette Berlin. |
| C_REP2 | REPURCHASE | I intend to shop at Galeries Lafayette Berlin in the future. |
| C_REP3 | REPURCAHSE | I will surely visit Galeries Lafayette Berlin in the future. |
| COM_A1 | AFFECTIVE COMMITMENT | How strongly are you attached to Galeries Lafayette Berlin? |
| COM_A2 | AFFECTIVE COMMITMENT | How strongly are you emotionally connected to Galeries Lafayette Berlin? |
| COM_A3 | AFFECTIVE COMMITMENT | As a customer I feel (close) attached to GL |
| COM_A4 | AFFECTIVE COMMITMENT | feel a strong emotional bond toward GLB |
| SAT_1 | SATISFACTION | I am very satisfied with Galeries Lafayette Berlin. |
| SAT_2 | SATISFACTION | Overall, I am very satisfied with Galeries Lafayette Berlin. |
| SAT_3 | SATISFACTION | How satisfied are you with Galeries Lafayette Berlin? |
| SAT_P1 | SATISFACTION EMPLOYEES | The employees are capable and professional. |
| SAT_P2 | SATISFACTION EMPLOYEES | The employees know best about their products. |
| SAT_P3 | SATISFACTION EMPLOYEES | The employees are well-informed. |
| SAT_P4 | SATISFACTION EMPLOYEES | The employees are always helpful. |
| SAT_P5 | SATISFACTION EMPLOYEES | The employees are willing to respond to my questions in detail. |
| SAT_P6 | SATISFACTION EMPLOYEES | The employees are friendly. |
| TRU_1 | TRUST | I have the feeling that I can completely rely on GL. |
| TRU_2 | TRUST | GLB will always be honest and trustful with me. |
| TRU_3 | TRUST | GL will treat me always fair as a customer |
# # omit all unanswered
# filter_all(survey, all_vars(. != 999))
# filter_all(survey, any_vars(. %in% c(999)))
#
# filter_all(select(survey,1:22,"SAT_1"), all_vars(. != 999))
# filter_all(select(survey,1:22,"SAT_1"), any_vars(. %in% c(999)))
#
# filter_all(data_img_EFA, all_vars(. != 999))
# filter_all(ges, any_vars(. %in% c(999)))# delete variables unused in analysis (see case study instructions):
survey <- survey |> select(-c("C_CR2", "SAT_P1", "SAT_P2", "SAT_P3", "SAT_P4", "SAT_P5", "SAT_P6", "TRU_1", "TRU_2", "TRU_3"))
# replace missing data (999) with NA
survey <- data.frame(sapply(survey,function(x) ifelse((x==999),NA,as.numeric(x))))# excluded image variables (in the first round of EFA we don't exclude any image variables...)
exclude=c()
# the full survey data (includes dependent and independent variables) with excluded image variables (in this first round of EFA we don't exclude anything)
survey_excl_img <- survey |> select(-exclude)
# the data we will use for EFA (images)
data_img_EFA <- survey_excl_img[1:(22-length(exclude))]# delete missing data (delete listwise)
data_img_EFA <- na.omit(data_img_EFA)
dim(survey)## [1] 553 35
dim(survey_excl_img)## [1] 553 35
dim(data_img_EFA)## [1] 385 22
#plot correlation matrix adjusting parameters to see previously identified groupings
corr_matrix <- cor(data_img_EFA)
corrplot(as.matrix(corr_matrix),
method = "color", #col = c("white","white","white","white","white", "lightgrey", "darkgrey", "black"),
order = "hclust", addrect = 10, rect.col="black", # rect.col="red",
addCoef.col = 'black', number.cex = .5,
tl.col ="black",
tl.cex = 0.80,
)Variables to look out for going forward:
Images 9 and 11 are alone
Pairs of images: (17,18), cluster exclusively together, have a very high correlation and similar correlation profiles meaning we might only want to keep one of them. Similar comment to a lesser degree for (6,7) and (16,19).
bart_spher(data_img_EFA)## Bartlett's Test of Sphericity
##
## Call: bart_spher(x = data_img_EFA)
##
## X2 = 6451.238
## df = 231
## p-value < 2.22e-16
The Bartlett Test tests the hypothesis that the sample originates from a population, where all variables are uncorrelated. This would not be good for factor analysis, we want this hypothesis to be rejected meaning p-value < 5%.
In our case we see that it is indeed rejected and that the data is not uncorrelated.
KMOTEST=KMOS(data_img_EFA)
print(KMOTEST, sort=T)##
## Kaiser-Meyer-Olkin Statistics
##
## Call: KMOS(x = data_img_EFA)
##
## Measures of Sampling Adequacy (MSA):
## Im2 Im6 Im1 Im20 Im14 Im10 Im7 Im4
## 0.8224640 0.8224827 0.8244624 0.8266391 0.8267452 0.8285789 0.8448231 0.8542604
## Im18 Im3 Im17 Im13 Im12 Im22 Im16 Im11
## 0.8550678 0.8640362 0.8644991 0.8722220 0.8789413 0.8793157 0.9092200 0.9113882
## Im21 Im8 Im9 Im19 Im5 Im15
## 0.9149654 0.9300079 0.9380091 0.9400714 0.9546668 0.9647563
##
## KMO-Criterion: 0.8770975
The KMO of 0.8770975 is above 0.6 which indicates the data is well suited for factor anlysis.
MSA_list <- data.table("Item"=names(KMOTEST$MSA), "MSA"=as.numeric(KMOTEST$MSA))
# Sort table
MSA_list<- MSA_list |>
setorder(cols = "MSA")
# Display table
MSA_list |>
stable() |>
row_spec(which(MSA_list[,2]<0.5), bold = T, color = "white", background = "#78BE20")| Item | MSA |
|---|---|
| Im2 | 0.82 |
| Im6 | 0.82 |
| Im1 | 0.82 |
| Im20 | 0.83 |
| Im14 | 0.83 |
| Im10 | 0.83 |
| Im7 | 0.84 |
| Im4 | 0.85 |
| Im18 | 0.86 |
| Im3 | 0.86 |
| Im17 | 0.86 |
| Im13 | 0.87 |
| Im12 | 0.88 |
| Im22 | 0.88 |
| Im16 | 0.91 |
| Im11 | 0.91 |
| Im21 | 0.91 |
| Im8 | 0.93 |
| Im9 | 0.94 |
| Im19 | 0.94 |
| Im5 | 0.95 |
| Im15 | 0.96 |
Variables with MSA values above 0.5 are suited for factor analysis. Presence of items with low MSA’s (<0.5) could also indicate that an important topic hasn’t been well covered in the questionnaire.
All variables have MSA above 0.5
EFA_PAF0 <- psych::fa(data_img_EFA, rotate="varimax", scores=TRUE)
# note: by default number of factors = 1 if it is not specified#display Scree-plot
plot(EFA_PAF0$e.values,xlab="Factor Number",
ylab="Eigenvalue",
main="Scree plot",
cex.lab=1.2,
cex.axis=1.2,
cex.main=1.8,
col = "#0099F8",
pch = 19)
abline(h=1, col = "#7F35B2")EFA_PAF0_kaiser_nb <- length(which(EFA_PAF0$e.values > 1))
EFA_PAF0_kaiser_nb## [1] 6
The Kaiser criterion suggests we should retain factors with eigenvalues bigger than 1.
There are 6 factors satisfying this condition.
#calculate total variance (does not change if number of factors change)
EFA_PAF0_EigenValue <- EFA_PAF0$e.values
EFA_PAF0_Variance <- EFA_PAF0_EigenValue / ncol(data_img_EFA) * 100
EFA_PAF0_SumVariance <- cumsum(EFA_PAF0_EigenValue / ncol(data_img_EFA))
EFA_PAF0_Total_Variance_Explained <- cbind("Factor number"=
seq(1, length.out=length(EFA_PAF0_EigenValue[EFA_PAF0_EigenValue>0])),
EigenValue = EFA_PAF0_EigenValue[EFA_PAF0_EigenValue>0],
Variance = EFA_PAF0_Variance[EFA_PAF0_EigenValue>0],
Total_Variance = EFA_PAF0_SumVariance[EFA_PAF0_EigenValue>0])
#display table
EFA_PAF0_Total_Variance_Explained |>
stable() | Factor number | EigenValue | Variance | Total_Variance |
|---|---|---|---|
| 1 | 8.98 | 40.81 | 0.41 |
| 2 | 2.47 | 11.21 | 0.52 |
| 3 | 1.56 | 7.10 | 0.59 |
| 4 | 1.46 | 6.62 | 0.66 |
| 5 | 1.25 | 5.67 | 0.71 |
| 6 | 1.15 | 5.22 | 0.77 |
| 7 | 0.81 | 3.68 | 0.80 |
| 8 | 0.71 | 3.23 | 0.84 |
| 9 | 0.57 | 2.58 | 0.86 |
| 10 | 0.46 | 2.08 | 0.88 |
| 11 | 0.36 | 1.64 | 0.90 |
| 12 | 0.33 | 1.51 | 0.91 |
| 13 | 0.29 | 1.34 | 0.93 |
| 14 | 0.28 | 1.29 | 0.94 |
| 15 | 0.25 | 1.13 | 0.95 |
| 16 | 0.23 | 1.04 | 0.96 |
| 17 | 0.20 | 0.92 | 0.97 |
| 18 | 0.19 | 0.85 | 0.98 |
| 19 | 0.16 | 0.72 | 0.99 |
| 20 | 0.12 | 0.53 | 0.99 |
| 21 | 0.10 | 0.46 | 1.00 |
| 22 | 0.08 | 0.37 | 1.00 |
With 6 factors we would explain 76.6310791% of total variance.
With 7 factors we would explain 80.3133487% of total variance.
# test eigenvalue calculation
factorloadings = EFA_PAF0$loadings[,1] # loadings 1st factor (default is nfactors = 1)
Eigenvalue = sum(factorloadings^2)
Eigenvalue## [1] 8.377985
# select nb of factors to test
nf = c(5,6,7,8)# perform multiple PAFs one for each factor number in selection
EFA_PAFn = list()
i=1
for (n in nf) {
# EFA_PAFn[[i]] <- n
EFA_PAFn[[i]] <- psych::fa(data_img_EFA, rotate="varimax", scores=TRUE, nfactors = n)
i=i+1
}
names(EFA_PAFn) <- nf#communalities for all selected number of factors
for (i in 1:length(nf)) {
cat("###### Number of factors =", nf[[i]], "{.unnumbered}" ,"\n")
EFA_PAFn_communalities <- data.table("Item"=names(EFA_PAFn[[i]]$communality),
"Communality"=as.numeric(EFA_PAFn[[i]]$communality))
# Sort table
EFA_PAFn_communalities <- EFA_PAFn_communalities |>
setorder(cols = "Communality")
# Display table
kbl <- EFA_PAFn_communalities |>
stable() |>
row_spec(which(EFA_PAFn_communalities[,1]<.3), bold = T, color = "white", background = "#78BE20")
print(kbl)
cat("\n\n")
# test communality calculation
variableloading = EFA_PAFn[[i]]$loadings["Im9",] # loadings 1st variable
communality = sum(variableloading^2)
print(paste0("Communality for Im9 =", communality))
cat("\n")
}| Item | Communality |
|---|---|
| Im9 | 0.41 |
| Im11 | 0.41 |
| Im18 | 0.43 |
| Im16 | 0.46 |
| Im6 | 0.50 |
| Im19 | 0.53 |
| Im17 | 0.54 |
| Im5 | 0.55 |
| Im15 | 0.63 |
| Im21 | 0.65 |
| Im14 | 0.66 |
| Im10 | 0.66 |
| Im7 | 0.69 |
| Im20 | 0.69 |
| Im12 | 0.71 |
| Im13 | 0.72 |
| Im2 | 0.76 |
| Im8 | 0.76 |
| Im22 | 0.81 |
| Im1 | 0.82 |
| Im3 | 0.86 |
| Im4 | 0.92 |
[1] “Communality for Im9 =0.405600881872799”
| Item | Communality |
|---|---|
| Im11 | 0.45 |
| Im9 | 0.46 |
| Im16 | 0.47 |
| Im19 | 0.52 |
| Im5 | 0.55 |
| Im18 | 0.57 |
| Im15 | 0.63 |
| Im21 | 0.65 |
| Im17 | 0.70 |
| Im13 | 0.70 |
| Im6 | 0.71 |
| Im12 | 0.73 |
| Im8 | 0.74 |
| Im14 | 0.76 |
| Im2 | 0.76 |
| Im10 | 0.78 |
| Im7 | 0.78 |
| Im20 | 0.79 |
| Im22 | 0.79 |
| Im1 | 0.84 |
| Im3 | 0.85 |
| Im4 | 0.92 |
[1] “Communality for Im9 =0.463399199002637”
| Item | Communality |
|---|---|
| Im11 | 0.44 |
| Im9 | 0.46 |
| Im16 | 0.47 |
| Im19 | 0.53 |
| Im5 | 0.54 |
| Im15 | 0.63 |
| Im21 | 0.65 |
| Im13 | 0.70 |
| Im18 | 0.71 |
| Im8 | 0.72 |
| Im6 | 0.76 |
| Im2 | 0.78 |
| Im22 | 0.79 |
| Im20 | 0.79 |
| Im14 | 0.81 |
| Im12 | 0.83 |
| Im7 | 0.85 |
| Im1 | 0.86 |
| Im3 | 0.86 |
| Im10 | 0.89 |
| Im17 | 0.95 |
| Im4 | 0.97 |
[1] “Communality for Im9 =0.455673655610471”
| Item | Communality |
|---|---|
| Im11 | 0.45 |
| Im9 | 0.46 |
| Im5 | 0.58 |
| Im19 | 0.62 |
| Im15 | 0.65 |
| Im21 | 0.65 |
| Im13 | 0.70 |
| Im8 | 0.72 |
| Im18 | 0.74 |
| Im6 | 0.76 |
| Im22 | 0.78 |
| Im16 | 0.80 |
| Im2 | 0.81 |
| Im20 | 0.81 |
| Im12 | 0.84 |
| Im7 | 0.85 |
| Im14 | 0.85 |
| Im3 | 0.86 |
| Im10 | 0.90 |
| Im17 | 0.93 |
| Im1 | 0.94 |
| Im4 | 0.97 |
[1] “Communality for Im9 =0.455554069181416”
Typically we should think about excluding variables with communalities below 0.3.
Based on the above, no variable should be excluded.
# loadings for all selected number of factors
for (i in 1:length(nf)) {
cat("###### Number of factors =", nf[[i]], "{.unnumbered}" ,"\n")
# print(EFA_PAFn[[i]]$loadings, cutoff=0.3)
# print(print_html(model_parameters(EFA_PAFn[[i]], loadings=T, threshold = 0.3, summary=T)))
kbl <- model_parameters(EFA_PAFn[[i]], loadings=T, threshold = 0.3, summary=T) |>
stable()
print(kbl)
cat("\n\n")
}| Variable | MR2 | MR5 | MR4 | MR1 | MR3 | Complexity | Uniqueness |
|---|---|---|---|---|---|---|---|
| Im1 | 0.85 | 1.31 | 0.18 | ||||
| Im2 | 0.83 | 1.23 | 0.24 | ||||
| Im3 | 0.83 | 1.55 | 0.14 | ||||
| Im4 | 0.87 | 1.46 | 0.08 | ||||
| Im5 | 0.64 | 1.78 | 0.45 | ||||
| Im6 | 0.67 | 1.22 | 0.50 | ||||
| Im7 | 0.79 | 1.20 | 0.31 | ||||
| Im8 | 0.84 | 1.16 | 0.24 | ||||
| Im9 | 0.43 | 0.39 | 2.76 | 0.59 | |||
| Im10 | 0.75 | 1.37 | 0.34 | ||||
| Im11 | 0.57 | 1.56 | 0.59 | ||||
| Im12 | 0.79 | 1.27 | 0.29 | ||||
| Im13 | 0.77 | 1.43 | 0.28 | ||||
| Im14 | 0.75 | 1.37 | 0.34 | ||||
| Im15 | 0.60 | 0.33 | 2.66 | 0.37 | |||
| Im16 | 0.48 | 0.37 | 2.77 | 0.54 | |||
| Im17 | 0.38 | 0.48 | 3.44 | 0.46 | |||
| Im18 | 0.31 | 0.43 | 3.42 | 0.57 | |||
| Im19 | 0.47 | 0.40 | 3.37 | 0.47 | |||
| Im20 | 0.78 | 1.27 | 0.31 | ||||
| Im21 | 0.74 | 1.41 | 0.35 | ||||
| Im22 | 0.81 | 1.51 | 0.19 |
| Variable | MR2 | MR5 | MR1 | MR4 | MR3 | MR6 | Complexity | Uniqueness |
|---|---|---|---|---|---|---|---|---|
| Im1 | 0.86 | 1.30 | 0.16 | |||||
| Im2 | 0.83 | 1.24 | 0.24 | |||||
| Im3 | 0.83 | 1.51 | 0.15 | |||||
| Im4 | 0.88 | 1.42 | 0.08 | |||||
| Im5 | 0.64 | 1.74 | 0.45 | |||||
| Im6 | 0.61 | 0.56 | 2.12 | 0.29 | ||||
| Im7 | 0.72 | 0.48 | 1.88 | 0.22 | ||||
| Im8 | 0.81 | 1.25 | 0.26 | |||||
| Im9 | 0.35 | 0.32 | 0.43 | 3.51 | 0.54 | |||
| Im10 | 0.80 | 1.42 | 0.22 | |||||
| Im11 | 0.59 | 1.62 | 0.55 | |||||
| Im12 | 0.79 | 1.34 | 0.27 | |||||
| Im13 | 0.73 | 1.66 | 0.30 | |||||
| Im14 | 0.80 | 1.42 | 0.24 | |||||
| Im15 | 0.60 | 2.76 | 0.37 | |||||
| Im16 | 0.48 | 0.37 | 2.78 | 0.53 | ||||
| Im17 | 0.35 | 0.31 | 0.39 | 0.54 | 3.66 | 0.30 | ||
| Im18 | 0.35 | 0.50 | 3.48 | 0.43 | ||||
| Im19 | 0.46 | 0.40 | 3.45 | 0.48 | ||||
| Im20 | 0.84 | 1.22 | 0.21 | |||||
| Im21 | 0.73 | 1.43 | 0.35 | |||||
| Im22 | 0.79 | 1.60 | 0.21 |
| Variable | MR5 | MR1 | MR3 | MR2 | MR4 | MR7 | MR6 | Complexity | Uniqueness |
|---|---|---|---|---|---|---|---|---|---|
| Im1 | 0.86 | 1.33 | 0.14 | ||||||
| Im2 | 0.83 | 1.27 | 0.22 | ||||||
| Im3 | 0.83 | 1.56 | 0.14 | ||||||
| Im4 | 0.90 | 1.40 | 0.03 | ||||||
| Im5 | 0.63 | 1.85 | 0.46 | ||||||
| Im6 | 0.83 | 1.25 | 0.24 | ||||||
| Im7 | 0.32 | 0.84 | 1.44 | 0.15 | |||||
| Im8 | 0.63 | 0.51 | 2.31 | 0.28 | |||||
| Im9 | 0.33 | 0.45 | 3.45 | 0.54 | |||||
| Im10 | 0.87 | 1.35 | 0.11 | ||||||
| Im11 | 0.58 | 1.72 | 0.56 | ||||||
| Im12 | 0.85 | 1.30 | 0.17 | ||||||
| Im13 | 0.72 | 1.81 | 0.30 | ||||||
| Im14 | 0.81 | 1.50 | 0.19 | ||||||
| Im15 | 0.59 | 2.97 | 0.37 | ||||||
| Im16 | 0.46 | 0.34 | 3.44 | 0.53 | |||||
| Im17 | 0.84 | 1.76 | 0.05 | ||||||
| Im18 | 0.72 | 1.85 | 0.29 | ||||||
| Im19 | 0.43 | 0.37 | 4.25 | 0.47 | |||||
| Im20 | 0.85 | 1.21 | 0.21 | ||||||
| Im21 | 0.73 | 1.44 | 0.35 | ||||||
| Im22 | 0.78 | 1.62 | 0.21 |
| Variable | MR1 | MR3 | MR4 | MR7 | MR2 | MR5 | MR6 | MR8 | Complexity | Uniqueness |
|---|---|---|---|---|---|---|---|---|---|---|
| Im1 | 0.88 | 1.45 | 0.06 | |||||||
| Im2 | 0.82 | 1.45 | 0.19 | |||||||
| Im3 | 0.81 | 1.66 | 0.14 | |||||||
| Im4 | 0.89 | 1.47 | 0.03 | |||||||
| Im5 | 0.65 | 1.84 | 0.42 | |||||||
| Im6 | 0.83 | 1.23 | 0.24 | |||||||
| Im7 | 0.84 | 0.30 | 1.40 | 0.15 | ||||||
| Im8 | 0.54 | 0.59 | 2.56 | 0.28 | ||||||
| Im9 | 0.33 | 0.46 | 3.34 | 0.54 | ||||||
| Im10 | 0.87 | 1.41 | 0.10 | |||||||
| Im11 | 0.58 | 1.72 | 0.55 | |||||||
| Im12 | 0.86 | 1.28 | 0.16 | |||||||
| Im13 | 0.72 | 1.78 | 0.30 | |||||||
| Im14 | 0.83 | 1.49 | 0.15 | |||||||
| Im15 | 0.47 | 0.39 | 4.81 | 0.35 | ||||||
| Im16 | 0.77 | 1.78 | 0.20 | |||||||
| Im17 | 0.82 | 1.82 | 0.07 | |||||||
| Im18 | 0.74 | 1.76 | 0.26 | |||||||
| Im19 | 0.30 | 0.54 | 3.68 | 0.38 | ||||||
| Im20 | 0.86 | 1.20 | 0.19 | |||||||
| Im21 | 0.73 | 1.44 | 0.35 | |||||||
| Im22 | 0.78 | 1.63 | 0.22 |
Factor loadings:
Based on the above we will prefer the 7 factor solution but we will no doubt have to exclude some variables.
Looking at the correlation matrix, we saw that variables Im16 and Im19 were highly correlated, we probably only need to exclude one of the two, Im19 has the lower communality of the two so we might consider eliminating that one.
Similarly Im17 and Im18 are highly correlated we might want to eliminate Im18 which has the lowest communality of the two, but they have adequately high loadings in the 7 factor solution so not a priority.
We might also exclude Im9 and Im15 as their communality is on the lower end and their loadings are spread out and quite weak. Also Im9 is problematic in both the 6 and 7 factor solution
Thurstone simple structure criteria:
Each row (variable) of the factor pattern matrix should have at least one zero
Each column (factor) should have at least r zero elements, and the zeros for one factor should be unique from the zeros for the other factors
For every pair of columns (factors), there should be at least r variables with a zero coefficient in one column and a non-zero coefficient in the other
When r > 3 every pair of columns (factors), should contain a large proportion of variables with zeros in both columns
For every pair of columns (factors), there should be only a small proportion of variables with non-zeros in both columns
# perform multiple PAFs one for each factor number in selection
EFA_PAFn_obl = list()
i=1
for (n in nf) {
# EFA_PAFn_obl[[i]] <- n
EFA_PAFn_obl[[i]] <- psych::fa(data_img_EFA, rotate="promax", scores=TRUE, nfactors = n)
i=i+1
}
names(EFA_PAFn_obl) <- nf
length(EFA_PAFn_obl)## [1] 4
#communalities for all selected number of factors
for (i in 1:length(nf)) {
cat("###### Number of factors =", nf[[i]], "{.unnumbered}" ,"\n")
EFA_PAFn_obl_communalities <- data.table("Item"=names(EFA_PAFn_obl[[i]]$communality),
"Communality"=as.numeric(EFA_PAFn_obl[[i]]$communality))
# Sort table
EFA_PAFn_obl_communalities <- EFA_PAFn_obl_communalities |>
setorder(cols = "Communality")
# Display table
kbl <- EFA_PAFn_obl_communalities |>
stable() |>
row_spec(which(EFA_PAFn_obl_communalities[,1]<.3), bold = T, color = "white", background = "#78BE20")
print(kbl)
cat("\n\n")
# test communality calculation
variableloading = EFA_PAFn_obl[[i]]$loadings["Im9",] # loadings 1st variable
communality = sum(variableloading^2)
print(paste0("Communality for Im9 =", communality))
cat("\n")
}| Item | Communality |
|---|---|
| Im9 | 0.41 |
| Im11 | 0.41 |
| Im18 | 0.43 |
| Im16 | 0.46 |
| Im6 | 0.50 |
| Im19 | 0.53 |
| Im17 | 0.54 |
| Im5 | 0.55 |
| Im15 | 0.63 |
| Im21 | 0.65 |
| Im14 | 0.66 |
| Im10 | 0.66 |
| Im7 | 0.69 |
| Im20 | 0.69 |
| Im12 | 0.71 |
| Im13 | 0.72 |
| Im2 | 0.76 |
| Im8 | 0.76 |
| Im22 | 0.81 |
| Im1 | 0.82 |
| Im3 | 0.86 |
| Im4 | 0.92 |
[1] “Communality for Im9 =0.272947652560888”
| Item | Communality |
|---|---|
| Im11 | 0.45 |
| Im9 | 0.46 |
| Im16 | 0.47 |
| Im19 | 0.52 |
| Im5 | 0.55 |
| Im18 | 0.57 |
| Im15 | 0.63 |
| Im21 | 0.65 |
| Im17 | 0.70 |
| Im13 | 0.70 |
| Im6 | 0.71 |
| Im12 | 0.73 |
| Im8 | 0.74 |
| Im14 | 0.76 |
| Im2 | 0.76 |
| Im10 | 0.78 |
| Im7 | 0.78 |
| Im20 | 0.79 |
| Im22 | 0.79 |
| Im1 | 0.84 |
| Im3 | 0.85 |
| Im4 | 0.92 |
[1] “Communality for Im9 =0.339338697735652”
| Item | Communality |
|---|---|
| Im11 | 0.44 |
| Im9 | 0.46 |
| Im16 | 0.47 |
| Im19 | 0.53 |
| Im5 | 0.54 |
| Im15 | 0.63 |
| Im21 | 0.65 |
| Im13 | 0.70 |
| Im18 | 0.71 |
| Im8 | 0.72 |
| Im6 | 0.76 |
| Im2 | 0.78 |
| Im22 | 0.79 |
| Im20 | 0.79 |
| Im14 | 0.81 |
| Im12 | 0.83 |
| Im7 | 0.85 |
| Im1 | 0.86 |
| Im3 | 0.86 |
| Im10 | 0.89 |
| Im17 | 0.95 |
| Im4 | 0.97 |
[1] “Communality for Im9 =0.279736181915467”
| Item | Communality |
|---|---|
| Im11 | 0.45 |
| Im9 | 0.46 |
| Im5 | 0.58 |
| Im19 | 0.62 |
| Im15 | 0.65 |
| Im21 | 0.65 |
| Im13 | 0.70 |
| Im8 | 0.72 |
| Im18 | 0.74 |
| Im6 | 0.76 |
| Im22 | 0.78 |
| Im16 | 0.80 |
| Im2 | 0.81 |
| Im20 | 0.81 |
| Im12 | 0.84 |
| Im7 | 0.85 |
| Im14 | 0.85 |
| Im3 | 0.86 |
| Im10 | 0.90 |
| Im17 | 0.93 |
| Im1 | 0.94 |
| Im4 | 0.97 |
[1] “Communality for Im9 =0.302814913694533”
# loadings for all selected number of factors
for (i in 1:length(nf)) {
cat("###### Number of factors =", nf[[i]], "{.unnumbered}" ,"\n")
# print(EFA_PAFn_obl[[i]]$loadings, cutoff=0.3)
# print(print_html(model_parameters(EFA_PAFn_obl[[i]], loadings=T, threshold = 0.3, summary=T)))
kbl <- model_parameters(EFA_PAFn_obl[[i]], loadings=T, threshold = 0.3, summary=T) |>
stable()
print(kbl)
cat("\n\n")
}| Variable | MR2 | MR5 | MR1 | MR4 | MR3 | Complexity | Uniqueness |
|---|---|---|---|---|---|---|---|
| Im1 | 1.07 | 1.06 | 0.18 | ||||
| Im2 | 1.07 | 1.07 | 0.24 | ||||
| Im3 | 1.00 | 1.03 | 0.14 | ||||
| Im4 | 1.07 | 1.03 | 0.08 | ||||
| Im5 | 0.75 | 1.03 | 0.45 | ||||
| Im6 | 0.73 | 1.11 | 0.50 | ||||
| Im7 | 0.87 | 1.14 | 0.31 | ||||
| Im8 | 0.91 | 1.01 | 0.24 | ||||
| Im9 | 0.36 | 0.37 | 2.10 | 0.59 | |||
| Im10 | 0.77 | 1.17 | 0.34 | ||||
| Im11 | 0.69 | 1.08 | 0.59 | ||||
| Im12 | 1.00 | 1.05 | 0.29 | ||||
| Im13 | 0.94 | 1.03 | 0.28 | ||||
| Im14 | 0.77 | 1.12 | 0.34 | ||||
| Im15 | 0.62 | 1.14 | 0.37 | ||||
| Im16 | 0.47 | 1.79 | 0.54 | ||||
| Im17 | 0.42 | 2.05 | 0.46 | ||||
| Im18 | 0.39 | 1.93 | 0.57 | ||||
| Im19 | 0.41 | 2.02 | 0.47 | ||||
| Im20 | 0.86 | 1.04 | 0.31 | ||||
| Im21 | 0.79 | 1.09 | 0.35 | ||||
| Im22 | 0.85 | 1.02 | 0.19 |
| Variable | MR2 | MR5 | MR1 | MR4 | MR3 | MR6 | Complexity | Uniqueness |
|---|---|---|---|---|---|---|---|---|
| Im1 | 1.05 | 1.06 | 0.16 | |||||
| Im2 | 1.03 | 1.07 | 0.24 | |||||
| Im3 | 0.99 | 1.03 | 0.15 | |||||
| Im4 | 1.06 | 1.05 | 0.08 | |||||
| Im5 | 0.74 | 1.03 | 0.45 | |||||
| Im6 | 0.52 | 0.68 | 2.22 | 0.29 | ||||
| Im7 | 0.65 | 0.56 | 2.24 | 0.22 | ||||
| Im8 | 0.80 | 1.05 | 0.26 | |||||
| Im9 | 0.48 | 1.95 | 0.54 | |||||
| Im10 | 0.81 | 1.23 | 0.22 | |||||
| Im11 | 0.67 | 1.15 | 0.55 | |||||
| Im12 | 0.91 | 1.03 | 0.27 | |||||
| Im13 | 0.79 | 1.09 | 0.30 | |||||
| Im14 | 0.80 | 1.18 | 0.24 | |||||
| Im15 | 0.60 | 1.18 | 0.37 | |||||
| Im16 | 0.46 | 1.81 | 0.53 | |||||
| Im17 | 0.57 | 1.97 | 0.30 | |||||
| Im18 | 0.54 | 1.91 | 0.43 | |||||
| Im19 | 0.39 | 2.15 | 0.48 | |||||
| Im20 | 0.92 | 1.07 | 0.21 | |||||
| Im21 | 0.76 | 1.07 | 0.35 | |||||
| Im22 | 0.80 | 1.04 | 0.21 |
| Variable | MR5 | MR1 | MR2 | MR3 | MR4 | MR7 | MR6 | Complexity | Uniqueness |
|---|---|---|---|---|---|---|---|---|---|
| Im1 | 1.08 | 1.06 | 0.14 | ||||||
| Im2 | 1.05 | 1.06 | 0.22 | ||||||
| Im3 | 1.00 | 1.02 | 0.14 | ||||||
| Im4 | 1.13 | 1.04 | 0.03 | ||||||
| Im5 | 0.72 | 1.02 | 0.46 | ||||||
| Im6 | 0.92 | 1.06 | 0.24 | ||||||
| Im7 | 0.89 | 1.06 | 0.15 | ||||||
| Im8 | 0.62 | 0.38 | 1.74 | 0.28 | |||||
| Im9 | 0.42 | 2.10 | 0.54 | ||||||
| Im10 | 1.04 | 1.03 | 0.11 | ||||||
| Im11 | 0.65 | 1.14 | 0.56 | ||||||
| Im12 | 1.01 | 1.04 | 0.17 | ||||||
| Im13 | 0.78 | 1.08 | 0.30 | ||||||
| Im14 | 0.94 | 1.01 | 0.19 | ||||||
| Im15 | 0.60 | 1.17 | 0.37 | ||||||
| Im16 | 0.40 | 2.69 | 0.53 | ||||||
| Im17 | 1.09 | 1.02 | 0.05 | ||||||
| Im18 | 0.92 | 1.02 | 0.29 | ||||||
| Im19 | 0.33 | 3.23 | 0.47 | ||||||
| Im20 | 0.94 | 1.05 | 0.21 | ||||||
| Im21 | 0.78 | 1.06 | 0.35 | ||||||
| Im22 | 0.81 | 1.05 | 0.21 |
| Variable | MR1 | MR3 | MR7 | MR2 | MR4 | MR5 | MR6 | MR8 | Complexity | Uniqueness |
|---|---|---|---|---|---|---|---|---|---|---|
| Im1 | 1.04 | 1.01 | 0.06 | |||||||
| Im2 | 0.95 | 1.02 | 0.19 | |||||||
| Im3 | 0.90 | 1.02 | 0.14 | |||||||
| Im4 | 1.03 | 1.03 | 0.03 | |||||||
| Im5 | 0.72 | 1.11 | 0.42 | |||||||
| Im6 | 0.98 | 1.06 | 0.24 | |||||||
| Im7 | 0.95 | 1.05 | 0.15 | |||||||
| Im8 | 0.43 | 0.49 | 2.39 | 0.28 | ||||||
| Im9 | 0.45 | 1.92 | 0.54 | |||||||
| Im10 | 0.97 | 1.01 | 0.10 | |||||||
| Im11 | 0.66 | 1.15 | 0.55 | |||||||
| Im12 | 1.04 | 1.05 | 0.16 | |||||||
| Im13 | 0.79 | 1.06 | 0.30 | |||||||
| Im14 | 0.92 | 1.02 | 0.15 | |||||||
| Im15 | 0.35 | 0.36 | 2.73 | 0.35 | ||||||
| Im16 | 1.02 | 1.03 | 0.20 | |||||||
| Im17 | 0.98 | 1.01 | 0.07 | |||||||
| Im18 | 0.90 | 1.01 | 0.26 | |||||||
| Im19 | 0.63 | 1.11 | 0.38 | |||||||
| Im20 | 0.98 | 1.09 | 0.19 | |||||||
| Im21 | 0.79 | 1.06 | 0.35 | |||||||
| Im22 | 0.82 | 1.06 | 0.22 |
7 factors: exclude 9, 15, 16, 19 6 factors: exclude 16, 17, 18, 19, 5 factors: exclude 17, 18
# # perform multiple variable selections
#
# exclude <- list(c("Im1","Im2","Im16", "Im19","Im15","Im9"),
# c("Im3","Im4","Im9", "Im15","Im11"))
#
# survey_excl_img2 = list()
# data_img_EFA2 = list()
#
# for (i in 1:length(exclude)){
# survey_excl_img2[[i]] <- survey |> select(-exclude[[i]])
# data_img_EFA2[[i]] <- survey_excl_img2[[i]][1:(22-length(exclude[[i]]))]
# # print(survey_excl_img2[[i]])
# }
#
# # survey_excl_img2[[1]]
# # survey_excl_img2[[2]]
# data_img_EFA2[[1]]
# data_img_EFA2[[2]]# excluded image variables
# candidates for 7 factors: "Im9",("Im11"),"Im15", "Im19", "Im16"
# candidates for 6 factors: "Im16","Im9", "Im19", ("Im11"), ("Im15"), ("Im18"),"Im17", "Im6"
exclude=c("Im9","Im15","Im8") # "Im16", "Im19","Im9","Im11","Im15"
# the full survey data (includes dependent and independent variables) with excluded image variables
survey_excl_img2 <- survey |> select(-exclude)
# the data we will use for EFA (images)
data_img_EFA2 <- survey_excl_img2[1:(22-length(exclude))]The excluded variables correspond to the following:
excludedvars <- filter(labels, Variable %in% exclude)[c("Variable","Label_short")]
excludedvars |>
stable()| Variable | Label_short |
|---|---|
| Im8 | Expertise in French Traditional Cuisine |
| Im9 | French Fashion |
| Im15 | Professional Selection of Brands |
# delete missing data
data_img_EFA2 <- na.omit(data_img_EFA2)
dim(survey)## [1] 553 35
dim(survey_excl_img2)## [1] 553 32
dim(data_img_EFA2)## [1] 394 19
#plot correlation matrix adjusting parameters to see previously identified groupings
corr_matrix <- cor(data_img_EFA2)
corrplot(as.matrix(corr_matrix),
method = "color", #col = c("white","white","white","white","white", "lightgrey", "darkgrey", "black"),
order = "hclust", addrect = 10, rect.col="black", # rect.col="red",
addCoef.col = 'black', number.cex = .5,
tl.col ="black",
tl.cex = 0.80,
)Here we have excluded variables: Im8, Im9, Im15 corresponding to Expertise in French Traditional Cuisine, French Fashion, Professional Selection of Brands respectively
Variables to look out for going forward: - Images 9 and 11 are alone - Pairs of images: (17,18), cluster exclusively together, have a very high correlation and similar correlation profiles meaning we might only want to keep one of them. Similar comment to a lesser degree for (6,7) and (16,19).
bart_spher(data_img_EFA2)## Bartlett's Test of Sphericity
##
## Call: bart_spher(x = data_img_EFA2)
##
## X2 = 5521.451
## df = 171
## p-value < 2.22e-16
The Bartlett Test tests the hypothesis that the sample originates from a population, where all variables are uncorrelated. This would not be good for factor analysis, we want this hypothesis to be rejected meaning p-value < 5%.
In our case we see that it is indeed rejected and that the data is not uncorrelated.
KMOTEST=KMOS(data_img_EFA2)
print(KMOTEST, sort=T)##
## Kaiser-Meyer-Olkin Statistics
##
## Call: KMOS(x = data_img_EFA2)
##
## Measures of Sampling Adequacy (MSA):
## Im6 Im10 Im7 Im14 Im2 Im1 Im20 Im18
## 0.7471329 0.7642565 0.7744268 0.7843674 0.7950011 0.7961197 0.8143469 0.8323628
## Im4 Im17 Im12 Im3 Im13 Im22 Im11 Im16
## 0.8394241 0.8427407 0.8483413 0.8497470 0.8567410 0.8730869 0.8958364 0.9007282
## Im21 Im19 Im5
## 0.9102753 0.9199391 0.9515411
##
## KMO-Criterion: 0.8416876
The KMO of 0.8416876 is above 0.6 which indicates the data is well suited for factor anlysis.
MSA_list <- data.table("Item"=names(KMOTEST$MSA), "MSA"=as.numeric(KMOTEST$MSA))
#Display table
MSA_list<- MSA_list |>
setorder(cols = "MSA")
MSA_list |>
stable() |>
row_spec(which(MSA_list[,2]<0.5), bold = T, color = "white", background = "#78BE20")| Item | MSA |
|---|---|
| Im6 | 0.75 |
| Im10 | 0.76 |
| Im7 | 0.77 |
| Im14 | 0.78 |
| Im2 | 0.80 |
| Im1 | 0.80 |
| Im20 | 0.81 |
| Im18 | 0.83 |
| Im4 | 0.84 |
| Im17 | 0.84 |
| Im12 | 0.85 |
| Im3 | 0.85 |
| Im13 | 0.86 |
| Im22 | 0.87 |
| Im11 | 0.90 |
| Im16 | 0.90 |
| Im21 | 0.91 |
| Im19 | 0.92 |
| Im5 | 0.95 |
Here we have excluded variables: Im8, Im9, Im15 corresponding to Expertise in French Traditional Cuisine, French Fashion, Professional Selection of Brands respectively
Variables with MSA values above 0.5 are suited for factor analysis. Presence of items with low MSA’s (<0.5) could also indicate that an important topic hasn’t been well covered in the questionnaire.
All variables have MSA above 0.5
EFA_PAF0 <- psych::fa(data_img_EFA2, rotate="varimax", scores=TRUE)
# note: by default number of factors = 1 if it is not specified#display Scree-plot
plot(EFA_PAF0$e.values,xlab="Factor Number",
ylab="Eigenvalue",
main="Scree plot",
cex.lab=1.2,
cex.axis=1.2,
cex.main=1.8,
col = "#0099F8",
pch = 19)
abline(h=1, col = "#7F35B2")Here we have excluded variables: Im8, Im9, Im15 corresponding to Expertise in French Traditional Cuisine, French Fashion, Professional Selection of Brands respectively
EFA_PAF0_kaiser_nb <- length(which(EFA_PAF0$e.values > 1))
EFA_PAF0_kaiser_nb## [1] 6
The Kaiser criterion suggests we should retain factors with eigenvalues bigger than 1.
There are 6 factors satisfying this condition.
#calculate total variance (does not change if number of factors change)
EFA_PAF0_EigenValue <- EFA_PAF0$e.values
EFA_PAF0_Variance <- EFA_PAF0_EigenValue / ncol(data_img_EFA2) * 100
EFA_PAF0_SumVariance <- cumsum(EFA_PAF0_EigenValue / ncol(data_img_EFA2))
EFA_PAF0_Total_Variance_Explained <- cbind("Factor number"=
seq(1, length.out=length(EFA_PAF0_EigenValue[EFA_PAF0_EigenValue>0])),
EigenValue = EFA_PAF0_EigenValue[EFA_PAF0_EigenValue>0],
Variance = EFA_PAF0_Variance[EFA_PAF0_EigenValue>0],
Total_Variance = EFA_PAF0_SumVariance[EFA_PAF0_EigenValue>0])
#display table
EFA_PAF0_Total_Variance_Explained |>
stable()| Factor number | EigenValue | Variance | Total_Variance |
|---|---|---|---|
| 1 | 7.71 | 40.57 | 0.41 |
| 2 | 2.01 | 10.58 | 0.51 |
| 3 | 1.54 | 8.10 | 0.59 |
| 4 | 1.44 | 7.58 | 0.67 |
| 5 | 1.20 | 6.30 | 0.73 |
| 6 | 1.06 | 5.56 | 0.79 |
| 7 | 0.80 | 4.21 | 0.83 |
| 8 | 0.68 | 3.60 | 0.87 |
| 9 | 0.50 | 2.65 | 0.89 |
| 10 | 0.34 | 1.81 | 0.91 |
| 11 | 0.32 | 1.67 | 0.93 |
| 12 | 0.30 | 1.58 | 0.94 |
| 13 | 0.23 | 1.20 | 0.95 |
| 14 | 0.21 | 1.10 | 0.97 |
| 15 | 0.19 | 1.02 | 0.98 |
| 16 | 0.16 | 0.84 | 0.98 |
| 17 | 0.12 | 0.62 | 0.99 |
| 18 | 0.11 | 0.57 | 1.00 |
| 19 | 0.08 | 0.43 | 1.00 |
Here we have excluded variables: Im8, Im9, Im15 corresponding to Expertise in French Traditional Cuisine, French Fashion, Professional Selection of Brands respectively
With 6 factors we would explain 78.6947762% of total variance.
With 7 factors we would explain 82.9058259% of total variance.
# test eigenvalue calculation
factorloadings = EFA_PAF0$loadings[,1] # loadings 1st factor (default is nfactors = 1)
Eigenvalue = sum(factorloadings^2)
Eigenvalue## [1] 7.109148
# select nb of factors to test
nf = c(5,6,7,8)# perform multiple PAFs one for each factor number in selection
EFA_PAFn = list()
i=1
for (n in nf) {
# EFA_PAFn[[i]] <- n
EFA_PAFn[[i]] <- psych::fa(data_img_EFA2, rotate="varimax", scores=TRUE, nfactors = n)
i=i+1
}
names(EFA_PAFn) <- nf#communalities for all selected number of factors
for (i in 1:length(nf)) {
cat("###### Number of factors =", nf[[i]], "{.unnumbered}" ,"\n")
EFA_PAFn_communalities <- data.table("Item"=names(EFA_PAFn[[i]]$communality),
"Communality"=as.numeric(EFA_PAFn[[i]]$communality))
# Sort table
EFA_PAFn_communalities <- EFA_PAFn_communalities |>
setorder(cols = "Communality")
# Display table
kbl <- EFA_PAFn_communalities |>
stable() |>
row_spec(which(EFA_PAFn_communalities[,1]<.3), bold = T, color = "white", background = "#78BE20")
print(kbl)
cat("\n\n")
# test communality calculation
variableloading = EFA_PAFn[[i]]$loadings["Im6",] # loadings 1st variable
communality = sum(variableloading^2)
print(paste0("Communality for Im6 =", communality))
cat("\n")
}| Item | Communality |
|---|---|
| Im11 | 0.41 |
| Im18 | 0.42 |
| Im16 | 0.42 |
| Im6 | 0.50 |
| Im19 | 0.51 |
| Im17 | 0.52 |
| Im5 | 0.55 |
| Im21 | 0.64 |
| Im10 | 0.66 |
| Im7 | 0.67 |
| Im14 | 0.70 |
| Im20 | 0.72 |
| Im13 | 0.72 |
| Im12 | 0.75 |
| Im2 | 0.78 |
| Im22 | 0.80 |
| Im1 | 0.84 |
| Im3 | 0.86 |
| Im4 | 0.92 |
[1] “Communality for Im6 =0.496673139129337”
| Item | Communality |
|---|---|
| Im16 | 0.42 |
| Im11 | 0.45 |
| Im19 | 0.51 |
| Im5 | 0.55 |
| Im6 | 0.64 |
| Im21 | 0.64 |
| Im18 | 0.65 |
| Im13 | 0.69 |
| Im10 | 0.71 |
| Im7 | 0.73 |
| Im12 | 0.74 |
| Im14 | 0.74 |
| Im20 | 0.78 |
| Im22 | 0.79 |
| Im2 | 0.80 |
| Im17 | 0.83 |
| Im3 | 0.86 |
| Im1 | 0.89 |
| Im4 | 0.92 |
[1] “Communality for Im6 =0.638799740882147”
| Item | Communality |
|---|---|
| Im16 | 0.43 |
| Im11 | 0.43 |
| Im19 | 0.51 |
| Im5 | 0.55 |
| Im21 | 0.64 |
| Im18 | 0.67 |
| Im13 | 0.69 |
| Im7 | 0.72 |
| Im14 | 0.78 |
| Im22 | 0.78 |
| Im20 | 0.79 |
| Im2 | 0.81 |
| Im3 | 0.86 |
| Im12 | 0.87 |
| Im1 | 0.91 |
| Im6 | 0.93 |
| Im4 | 0.97 |
| Im10 | 0.97 |
| Im17 | 1.00 |
[1] “Communality for Im6 =0.931925021212407”
| Item | Communality |
|---|---|
| Im11 | 0.43 |
| Im5 | 0.58 |
| Im21 | 0.64 |
| Im16 | 0.67 |
| Im18 | 0.68 |
| Im13 | 0.69 |
| Im7 | 0.69 |
| Im19 | 0.70 |
| Im2 | 0.76 |
| Im14 | 0.78 |
| Im22 | 0.78 |
| Im20 | 0.81 |
| Im3 | 0.86 |
| Im12 | 0.87 |
| Im4 | 0.97 |
| Im6 | 0.99 |
| Im10 | 1.00 |
| Im17 | 1.00 |
| Im1 | 1.00 |
[1] “Communality for Im6 =0.990898460352201”
Typically we should think about excluding variables with communalities below 0.3.
Based on the above, no variable should be excluded.
# loadings for all selected number of factors
for (i in 1:length(nf)) {
cat("###### Number of factors =", nf[[i]], "{.unnumbered}" ,"\n")
# print(EFA_PAFn[[i]]$loadings, cutoff=0.3)
# print(print_html(model_parameters(EFA_PAFn[[i]], loadings=T, threshold = 0.3, summary=T)))
kbl <- model_parameters(EFA_PAFn[[i]], loadings=T, threshold = 0.3, summary=T) |>
stable()
print(kbl)
cat("\n\n")
}| Variable | MR1 | MR2 | MR4 | MR5 | MR3 | Complexity | Uniqueness |
|---|---|---|---|---|---|---|---|
| Im1 | 0.85 | 1.35 | 0.16 | ||||
| Im2 | 0.83 | 1.27 | 0.22 | ||||
| Im3 | 0.84 | 1.44 | 0.14 | ||||
| Im4 | 0.89 | 1.36 | 0.08 | ||||
| Im5 | 0.65 | 1.66 | 0.45 | ||||
| Im6 | 0.67 | 1.23 | 0.50 | ||||
| Im7 | 0.78 | 1.20 | 0.33 | ||||
| Im10 | 0.74 | 1.42 | 0.34 | ||||
| Im11 | 0.58 | 1.49 | 0.59 | ||||
| Im12 | 0.82 | 1.22 | 0.25 | ||||
| Im13 | 0.77 | 1.44 | 0.28 | ||||
| Im14 | 0.77 | 1.39 | 0.30 | ||||
| Im16 | 0.40 | 0.41 | 3.03 | 0.58 | |||
| Im17 | 0.30 | 0.43 | 0.39 | 3.76 | 0.48 | ||
| Im18 | 0.39 | 0.32 | 3.81 | 0.58 | |||
| Im19 | 0.42 | 0.43 | 3.53 | 0.49 | |||
| Im20 | 0.80 | 1.23 | 0.28 | ||||
| Im21 | 0.74 | 1.39 | 0.36 | ||||
| Im22 | 0.81 | 1.49 | 0.20 |
| Variable | MR1 | MR2 | MR3 | MR4 | MR5 | MR6 | Complexity | Uniqueness |
|---|---|---|---|---|---|---|---|---|
| Im1 | 0.86 | 1.40 | 0.11 | |||||
| Im2 | 0.83 | 1.33 | 0.20 | |||||
| Im3 | 0.85 | 1.43 | 0.14 | |||||
| Im4 | 0.89 | 1.35 | 0.08 | |||||
| Im5 | 0.65 | 1.63 | 0.45 | |||||
| Im6 | 0.73 | 1.40 | 0.36 | |||||
| Im7 | 0.81 | 1.24 | 0.27 | |||||
| Im10 | 0.70 | 0.32 | 1.95 | 0.29 | ||||
| Im11 | 0.61 | 1.46 | 0.55 | |||||
| Im12 | 0.80 | 1.31 | 0.26 | |||||
| Im13 | 0.71 | 1.80 | 0.31 | |||||
| Im14 | 0.73 | 0.32 | 1.85 | 0.26 | ||||
| Im16 | 0.41 | 0.39 | 3.16 | 0.58 | ||||
| Im17 | 0.74 | 2.15 | 0.17 | |||||
| Im18 | 0.66 | 2.10 | 0.35 | |||||
| Im19 | 0.43 | 0.39 | 3.93 | 0.49 | ||||
| Im20 | 0.84 | 1.21 | 0.22 | |||||
| Im21 | 0.73 | 1.43 | 0.36 | |||||
| Im22 | 0.79 | 1.54 | 0.21 |
| Variable | MR1 | MR3 | MR4 | MR5 | MR2 | MR6 | MR7 | Complexity | Uniqueness |
|---|---|---|---|---|---|---|---|---|---|
| Im1 | 0.87 | 1.40 | 0.09 | ||||||
| Im2 | 0.83 | 1.35 | 0.19 | ||||||
| Im3 | 0.84 | 1.46 | 0.14 | ||||||
| Im4 | 0.92 | 1.33 | 0.03 | ||||||
| Im5 | 0.64 | 1.73 | 0.45 | ||||||
| Im6 | 0.93 | 1.17 | 0.07 | ||||||
| Im7 | 0.33 | 0.75 | 1.62 | 0.28 | |||||
| Im10 | 0.92 | 1.32 | 0.03 | ||||||
| Im11 | 0.57 | 1.70 | 0.57 | ||||||
| Im12 | 0.88 | 1.23 | 0.13 | ||||||
| Im13 | 0.72 | 1.76 | 0.31 | ||||||
| Im14 | 0.77 | 0.30 | 1.67 | 0.22 | |||||
| Im16 | 0.38 | 0.37 | 3.99 | 0.57 | |||||
| Im17 | 0.88 | 1.60 | 0.00 | ||||||
| Im18 | 0.70 | 1.84 | 0.33 | ||||||
| Im19 | 0.40 | 0.37 | 4.52 | 0.49 | |||||
| Im20 | 0.85 | 1.19 | 0.21 | ||||||
| Im21 | 0.73 | 1.43 | 0.36 | ||||||
| Im22 | 0.79 | 1.55 | 0.22 |
| Variable | MR1 | MR3 | MR4 | MR5 | MR2 | MR7 | MR6 | MR8 | Complexity | Uniqueness |
|---|---|---|---|---|---|---|---|---|---|---|
| Im1 | 0.91 | 1.44 | 0.00 | |||||||
| Im2 | 0.78 | 1.56 | 0.24 | |||||||
| Im3 | 0.82 | 1.63 | 0.14 | |||||||
| Im4 | 0.89 | 1.46 | 0.03 | |||||||
| Im5 | 0.66 | 1.78 | 0.42 | |||||||
| Im6 | 0.96 | 1.15 | 0.01 | |||||||
| Im7 | 0.34 | 0.72 | 1.69 | 0.31 | ||||||
| Im10 | 0.93 | 1.32 | 0.00 | |||||||
| Im11 | 0.57 | 1.71 | 0.57 | |||||||
| Im12 | 0.89 | 1.22 | 0.13 | |||||||
| Im13 | 0.72 | 1.76 | 0.31 | |||||||
| Im14 | 0.77 | 1.68 | 0.22 | |||||||
| Im16 | 0.68 | 2.03 | 0.33 | |||||||
| Im17 | 0.88 | 1.65 | 0.00 | |||||||
| Im18 | 0.70 | 1.84 | 0.32 | |||||||
| Im19 | 0.64 | 2.71 | 0.30 | |||||||
| Im20 | 0.86 | 1.19 | 0.19 | |||||||
| Im21 | 0.73 | 1.44 | 0.36 | |||||||
| Im22 | 0.79 | 1.56 | 0.22 |
Here we have excluded variables: Im8, Im9, Im15 corresponding to Expertise in French Traditional Cuisine, French Fashion, Professional Selection of Brands respectively
Factor loadings:
Based on the above we will prefer the 7 factor solution but we will no doubt have to exclude some variables, potentially 19 as it also has the lower communality than Im16 and probably also factor 9 as it also has low communality
Thurstone simple structure criteria:
Each row (variable) of the factor pattern matrix should have at least one zero
Each column (factor) should have at least r zero elements, and the zeros for one factor should be unique from the zeros for the other factors
For every pair of columns (factors), there should be at least r variables with a zero coefficient in one column and a non-zero coefficient in the other
When r > 3 every pair of columns (factors), should contain a large proportion of variables with zeros in both columns
For every pair of columns (factors), there should be only a small proportion of variables with non-zeros in both columns
# perform multiple PAFs one for each factor number in selection
EFA_PAFn_obl = list()
i=1
for (n in nf) {
# EFA_PAFn_obl[[i]] <- n
EFA_PAFn_obl[[i]] <- psych::fa(data_img_EFA2, rotate="promax", scores=TRUE, nfactors = n)
i=i+1
}
names(EFA_PAFn_obl) <- nf
length(EFA_PAFn_obl)## [1] 4
#communalities for all selected number of factors
for (i in 1:length(nf)) {
cat("###### Number of factors =", nf[[i]], "{.unnumbered}" ,"\n")
EFA_PAFn_obl_communalities <- data.table("Item"=names(EFA_PAFn_obl[[i]]$communality),
"Communality"=as.numeric(EFA_PAFn_obl[[i]]$communality))
# Sort table
EFA_PAFn_obl_communalities <- EFA_PAFn_obl_communalities |>
setorder(cols = "Communality")
# Display table
kbl <- EFA_PAFn_obl_communalities |>
stable() |>
row_spec(which(EFA_PAFn_obl_communalities[,1]<.3), bold = T, color = "white", background = "#78BE20")
print(kbl)
cat("\n\n")
# test communality calculation
variableloading = EFA_PAFn_obl[[i]]$loadings["Im6",] # loadings 1st variable
communality = sum(variableloading^2)
print(paste0("Communality for Im6 =", communality))
cat("\n")
}| Item | Communality |
|---|---|
| Im11 | 0.41 |
| Im18 | 0.42 |
| Im16 | 0.42 |
| Im6 | 0.50 |
| Im19 | 0.51 |
| Im17 | 0.52 |
| Im5 | 0.55 |
| Im21 | 0.64 |
| Im10 | 0.66 |
| Im7 | 0.67 |
| Im14 | 0.70 |
| Im20 | 0.72 |
| Im13 | 0.72 |
| Im12 | 0.75 |
| Im2 | 0.78 |
| Im22 | 0.80 |
| Im1 | 0.84 |
| Im3 | 0.86 |
| Im4 | 0.92 |
[1] “Communality for Im6 =0.547199381232095”
| Item | Communality |
|---|---|
| Im16 | 0.42 |
| Im11 | 0.45 |
| Im19 | 0.51 |
| Im5 | 0.55 |
| Im6 | 0.64 |
| Im21 | 0.64 |
| Im18 | 0.65 |
| Im13 | 0.69 |
| Im10 | 0.71 |
| Im7 | 0.73 |
| Im12 | 0.74 |
| Im14 | 0.74 |
| Im20 | 0.78 |
| Im22 | 0.79 |
| Im2 | 0.80 |
| Im17 | 0.83 |
| Im3 | 0.86 |
| Im1 | 0.89 |
| Im4 | 0.92 |
[1] “Communality for Im6 =0.833006250441541”
| Item | Communality |
|---|---|
| Im16 | 0.43 |
| Im11 | 0.43 |
| Im19 | 0.51 |
| Im5 | 0.55 |
| Im21 | 0.64 |
| Im18 | 0.67 |
| Im13 | 0.69 |
| Im7 | 0.72 |
| Im14 | 0.78 |
| Im22 | 0.78 |
| Im20 | 0.79 |
| Im2 | 0.81 |
| Im3 | 0.86 |
| Im12 | 0.87 |
| Im1 | 0.91 |
| Im6 | 0.93 |
| Im4 | 0.97 |
| Im10 | 0.97 |
| Im17 | 1.00 |
[1] “Communality for Im6 =0.971113915290573”
| Item | Communality |
|---|---|
| Im11 | 0.43 |
| Im5 | 0.58 |
| Im21 | 0.64 |
| Im16 | 0.67 |
| Im18 | 0.68 |
| Im13 | 0.69 |
| Im7 | 0.69 |
| Im19 | 0.70 |
| Im2 | 0.76 |
| Im14 | 0.78 |
| Im22 | 0.78 |
| Im20 | 0.81 |
| Im3 | 0.86 |
| Im12 | 0.87 |
| Im4 | 0.97 |
| Im6 | 0.99 |
| Im10 | 1.00 |
| Im17 | 1.00 |
| Im1 | 1.00 |
[1] “Communality for Im6 =1.14058133882705”
# loadings for all selected number of factors
test = list()
for (i in 1:length(nf)) {
cat("###### Number of factors =", nf[[i]], "{.unnumbered}" ,"\n")
# print(EFA_PAFn_obl[[i]]$loadings, cutoff=0.3)
# print(print_html(model_parameters(EFA_PAFn_obl[[i]], loadings=T, threshold = 0.3, summary=T)))
kbl <- model_parameters(EFA_PAFn_obl[[i]], loadings=T, threshold = 0.3, summary=T) |>
stable()
print(kbl)
cat("\n\n")
}| Variable | MR1 | MR2 | MR5 | MR4 | MR3 | Complexity | Uniqueness |
|---|---|---|---|---|---|---|---|
| Im1 | 1.06 | 1.05 | 0.16 | ||||
| Im2 | 1.06 | 1.07 | 0.22 | ||||
| Im3 | 1.05 | 1.04 | 0.14 | ||||
| Im4 | 1.11 | 1.05 | 0.08 | ||||
| Im5 | 0.77 | 1.03 | 0.45 | ||||
| Im6 | 0.72 | 1.12 | 0.50 | ||||
| Im7 | 0.85 | 1.15 | 0.33 | ||||
| Im10 | 0.75 | 1.21 | 0.34 | ||||
| Im11 | 0.68 | 1.09 | 0.59 | ||||
| Im12 | 1.00 | 1.04 | 0.25 | ||||
| Im13 | 0.89 | 1.02 | 0.28 | ||||
| Im14 | 0.78 | 1.14 | 0.30 | ||||
| Im16 | 0.33 | 0.36 | 2.14 | 0.58 | |||
| Im17 | 0.34 | 2.56 | 0.48 | ||||
| Im18 | 0.31 | 2.71 | 0.58 | ||||
| Im19 | 0.32 | 0.36 | 2.28 | 0.49 | |||
| Im20 | 0.88 | 1.07 | 0.28 | ||||
| Im21 | 0.78 | 1.06 | 0.36 | ||||
| Im22 | 0.84 | 1.02 | 0.20 |
| Variable | MR1 | MR2 | MR3 | MR5 | MR4 | MR6 | Complexity | Uniqueness |
|---|---|---|---|---|---|---|---|---|
| Im1 | 1.04 | 1.05 | 0.11 | |||||
| Im2 | 1.00 | 1.04 | 0.20 | |||||
| Im3 | 1.02 | 1.05 | 0.14 | |||||
| Im4 | 1.08 | 1.05 | 0.08 | |||||
| Im5 | 0.76 | 1.03 | 0.45 | |||||
| Im6 | 0.84 | 1.39 | 0.36 | |||||
| Im7 | 0.91 | 1.18 | 0.27 | |||||
| Im10 | 0.68 | 1.69 | 0.29 | |||||
| Im11 | 0.67 | 1.05 | 0.55 | |||||
| Im12 | 0.91 | 1.06 | 0.26 | |||||
| Im13 | 0.77 | 1.22 | 0.31 | |||||
| Im14 | 0.71 | 1.55 | 0.26 | |||||
| Im16 | 0.33 | 0.33 | 2.12 | 0.58 | ||||
| Im17 | 0.77 | 1.14 | 0.17 | |||||
| Im18 | 0.69 | 1.14 | 0.35 | |||||
| Im19 | 0.33 | 2.58 | 0.49 | |||||
| Im20 | 0.91 | 1.08 | 0.22 | |||||
| Im21 | 0.75 | 1.06 | 0.36 | |||||
| Im22 | 0.80 | 1.04 | 0.21 |
| Variable | MR1 | MR3 | MR5 | MR4 | MR2 | MR6 | MR7 | Complexity | Uniqueness |
|---|---|---|---|---|---|---|---|---|---|
| Im1 | 1.07 | 1.05 | 0.09 | ||||||
| Im2 | 1.02 | 1.03 | 0.19 | ||||||
| Im3 | 1.01 | 1.02 | 0.14 | ||||||
| Im4 | 1.14 | 1.05 | 0.03 | ||||||
| Im5 | 0.73 | 1.02 | 0.45 | ||||||
| Im6 | 0.98 | 1.04 | 0.07 | ||||||
| Im7 | 0.73 | 1.16 | 0.28 | ||||||
| Im10 | 1.10 | 1.03 | 0.03 | ||||||
| Im11 | 0.60 | 1.16 | 0.57 | ||||||
| Im12 | 1.00 | 1.03 | 0.13 | ||||||
| Im13 | 0.75 | 1.11 | 0.31 | ||||||
| Im14 | 0.87 | 1.04 | 0.22 | ||||||
| Im16 | 3.60 | 0.57 | |||||||
| Im17 | 1.12 | 1.02 | 0.00 | ||||||
| Im18 | 0.86 | 1.03 | 0.33 | ||||||
| Im19 | 3.47 | 0.49 | |||||||
| Im20 | 0.94 | 1.04 | 0.21 | ||||||
| Im21 | 0.77 | 1.05 | 0.36 | ||||||
| Im22 | 0.82 | 1.03 | 0.22 |
| Variable | MR1 | MR3 | MR4 | MR2 | MR5 | MR6 | MR7 | MR8 | Complexity | Uniqueness |
|---|---|---|---|---|---|---|---|---|---|---|
| Im1 | 1.03 | 1.01 | 0.00 | |||||||
| Im2 | 0.86 | 1.01 | 0.24 | |||||||
| Im3 | 0.90 | 1.02 | 0.14 | |||||||
| Im4 | 1.02 | 1.03 | 0.03 | |||||||
| Im5 | 0.73 | 1.09 | 0.42 | |||||||
| Im6 | 1.06 | 1.03 | 0.01 | |||||||
| Im7 | 0.72 | 1.14 | 0.31 | |||||||
| Im10 | 1.05 | 1.02 | 0.00 | |||||||
| Im11 | 0.60 | 1.15 | 0.57 | |||||||
| Im12 | 1.02 | 1.04 | 0.13 | |||||||
| Im13 | 0.75 | 1.09 | 0.31 | |||||||
| Im14 | 0.82 | 1.03 | 0.22 | |||||||
| Im16 | 0.80 | 1.02 | 0.33 | |||||||
| Im17 | 1.03 | 1.01 | 0.00 | |||||||
| Im18 | 0.81 | 1.00 | 0.32 | |||||||
| Im19 | 0.72 | 1.04 | 0.30 | |||||||
| Im20 | 0.97 | 1.09 | 0.19 | |||||||
| Im21 | 0.77 | 1.05 | 0.36 | |||||||
| Im22 | 0.82 | 1.04 | 0.22 |
Here we have excluded variables: Im8, Im9, Im15 corresponding to Expertise in French Traditional Cuisine, French Fashion, Professional Selection of Brands respectively
We test whether the constructs found in the exploratory phase adequately describe what is going on.
# no excluded variables
CFA_model_img_6f <- "
DECO =~ Im3 + Im4 + Im5
FRENCH =~ Im6 + Im7 + Im8 + Im10 + Im14
ATMOS =~ Im20 + Im21 + Im22
QUAL =~ Im11 + Im12 + Im13
CHOICE =~ Im1 + Im2 + Im15 + Im16 + Im19
BRAND =~ Im17 + Im18 + Im9
"
# # excluded variables: Im9, Im15, Im16, Im19
# CFA_model_img_6f <- "
# QUAL =~ Im11 + Im12 + Im13
# FRENCH =~ Im6 + Im7 + Im8 + Im10 + Im14
# ATMOS =~ Im20 + Im21 + Im22
# DECO =~ Im3 + Im4 + Im5
# CHOICE =~ Im1 + Im2
# BRAND =~ Im17 + Im18
# "
# # excluded variables: Im9, Im15, Im16, Im19, Im8
# CFA_model_img_6f <- "
# QUAL =~ Im11 + Im12 + Im13
# FRENCH =~ Im6 + Im7 + Im10 + Im14
# ATMOS =~ Im20 + Im21 + Im22
# DECO =~ Im3 + Im4 + Im5
# CHOICE =~ Im1 + Im2
# BRAND =~ Im17 + Im18
# "
# CFA_fit_img <- cfa(CFA_model_img_6f, data=data_img_EFA, missing="ML")
CFA_fit_img_6f <- cfa(CFA_model_img_6f, data=survey, missing="ML")
summary(CFA_fit_img_6f, fit.measures=TRUE, standardized=TRUE)## lavaan 0.6.15 ended normally after 110 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 81
##
## Number of observations 553
## Number of missing patterns 87
##
## Model Test User Model:
##
## Test statistic 1442.584
## Degrees of freedom 194
## P-value (Chi-square) 0.000
##
## Model Test Baseline Model:
##
## Test statistic 8838.959
## Degrees of freedom 231
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.855
## Tucker-Lewis Index (TLI) 0.827
##
## Robust Comparative Fit Index (CFI) 0.854
## Robust Tucker-Lewis Index (TLI) 0.827
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -15479.697
## Loglikelihood unrestricted model (H1) -14758.405
##
## Akaike (AIC) 31121.394
## Bayesian (BIC) 31470.938
## Sample-size adjusted Bayesian (SABIC) 31213.808
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.108
## 90 Percent confidence interval - lower 0.103
## 90 Percent confidence interval - upper 0.113
## P-value H_0: RMSEA <= 0.050 0.000
## P-value H_0: RMSEA >= 0.080 1.000
##
## Robust RMSEA 0.110
## 90 Percent confidence interval - lower 0.105
## 90 Percent confidence interval - upper 0.116
## P-value H_0: Robust RMSEA <= 0.050 0.000
## P-value H_0: Robust RMSEA >= 0.080 1.000
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.092
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Observed
## Observed information based on Hessian
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## DECO =~
## Im3 1.000 1.236 0.936
## Im4 1.057 0.025 42.551 0.000 1.307 0.970
## Im5 0.820 0.034 23.857 0.000 1.013 0.761
## FRENCH =~
## Im6 1.000 0.642 0.535
## Im7 1.219 0.106 11.525 0.000 0.783 0.644
## Im8 1.244 0.099 12.567 0.000 0.799 0.755
## Im10 1.251 0.095 13.133 0.000 0.803 0.914
## Im14 1.244 0.095 13.142 0.000 0.799 0.929
## ATMOS =~
## Im20 1.000 1.268 0.848
## Im21 0.848 0.041 20.879 0.000 1.075 0.785
## Im22 1.053 0.046 22.697 0.000 1.335 0.873
## QUAL =~
## Im11 1.000 0.703 0.615
## Im12 1.410 0.094 15.050 0.000 0.991 0.872
## Im13 1.465 0.105 13.982 0.000 1.030 0.855
## CHOICE =~
## Im1 1.000 1.232 0.926
## Im2 0.942 0.027 34.780 0.000 1.160 0.902
## Im15 0.720 0.036 20.097 0.000 0.887 0.740
## Im16 0.567 0.041 13.849 0.000 0.699 0.579
## Im19 0.540 0.038 14.310 0.000 0.666 0.592
## BRAND =~
## Im17 1.000 1.184 0.952
## Im18 1.025 0.038 27.280 0.000 1.214 0.868
## Im9 0.540 0.047 11.386 0.000 0.640 0.474
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## DECO ~~
## FRENCH 0.344 0.046 7.416 0.000 0.434 0.434
## ATMOS 0.730 0.082 8.901 0.000 0.466 0.466
## QUAL 0.409 0.051 8.040 0.000 0.471 0.471
## CHOICE 0.782 0.079 9.940 0.000 0.514 0.514
## BRAND 0.778 0.076 10.268 0.000 0.531 0.531
## FRENCH ~~
## ATMOS 0.265 0.045 5.888 0.000 0.326 0.326
## QUAL 0.206 0.030 6.812 0.000 0.456 0.456
## CHOICE 0.299 0.044 6.737 0.000 0.378 0.378
## BRAND 0.277 0.042 6.547 0.000 0.364 0.364
## ATMOS ~~
## QUAL 0.373 0.053 7.021 0.000 0.419 0.419
## CHOICE 0.767 0.083 9.216 0.000 0.491 0.491
## BRAND 0.792 0.081 9.797 0.000 0.528 0.528
## QUAL ~~
## CHOICE 0.460 0.054 8.585 0.000 0.531 0.531
## BRAND 0.483 0.053 9.113 0.000 0.581 0.581
## CHOICE ~~
## BRAND 0.864 0.078 11.040 0.000 0.592 0.592
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .Im3 4.994 0.056 88.528 0.000 4.994 3.785
## .Im4 4.997 0.057 86.919 0.000 4.997 3.709
## .Im5 5.034 0.057 87.796 0.000 5.034 3.785
## .Im6 5.824 0.051 113.338 0.000 5.824 4.849
## .Im7 5.751 0.053 109.497 0.000 5.751 4.727
## .Im8 6.000 0.045 133.008 0.000 6.000 5.671
## .Im10 6.100 0.037 163.041 0.000 6.100 6.945
## .Im14 6.139 0.037 166.909 0.000 6.139 7.138
## .Im20 4.672 0.064 73.182 0.000 4.672 3.124
## .Im21 5.139 0.058 87.973 0.000 5.139 3.751
## .Im22 4.278 0.065 65.391 0.000 4.278 2.798
## .Im11 5.653 0.049 115.277 0.000 5.653 4.943
## .Im12 5.666 0.049 116.095 0.000 5.666 4.983
## .Im13 5.448 0.052 105.630 0.000 5.448 4.525
## .Im1 4.792 0.057 84.316 0.000 4.792 3.601
## .Im2 4.861 0.055 88.357 0.000 4.861 3.779
## .Im15 5.090 0.051 99.219 0.000 5.090 4.246
## .Im16 5.130 0.052 98.387 0.000 5.130 4.251
## .Im19 5.146 0.048 106.829 0.000 5.146 4.578
## .Im17 5.025 0.053 94.490 0.000 5.025 4.038
## .Im18 4.595 0.060 76.460 0.000 4.595 3.286
## .Im9 5.075 0.058 87.318 0.000 5.075 3.757
## DECO 0.000 0.000 0.000
## FRENCH 0.000 0.000 0.000
## ATMOS 0.000 0.000 0.000
## QUAL 0.000 0.000 0.000
## CHOICE 0.000 0.000 0.000
## BRAND 0.000 0.000 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .Im3 0.215 0.024 8.776 0.000 0.215 0.123
## .Im4 0.108 0.024 4.439 0.000 0.108 0.060
## .Im5 0.744 0.049 15.192 0.000 0.744 0.421
## .Im6 1.030 0.066 15.665 0.000 1.030 0.714
## .Im7 0.867 0.059 14.739 0.000 0.867 0.586
## .Im8 0.482 0.034 14.159 0.000 0.482 0.430
## .Im10 0.127 0.013 9.840 0.000 0.127 0.164
## .Im14 0.101 0.012 8.329 0.000 0.101 0.137
## .Im20 0.629 0.061 10.379 0.000 0.629 0.281
## .Im21 0.721 0.057 12.668 0.000 0.721 0.384
## .Im22 0.554 0.063 8.781 0.000 0.554 0.237
## .Im11 0.814 0.055 14.805 0.000 0.814 0.622
## .Im12 0.310 0.039 7.857 0.000 0.310 0.240
## .Im13 0.390 0.044 8.777 0.000 0.390 0.269
## .Im1 0.253 0.035 7.312 0.000 0.253 0.143
## .Im2 0.308 0.033 9.422 0.000 0.308 0.186
## .Im15 0.651 0.048 13.673 0.000 0.651 0.453
## .Im16 0.968 0.065 14.927 0.000 0.968 0.664
## .Im19 0.820 0.055 14.954 0.000 0.820 0.649
## .Im17 0.146 0.036 4.039 0.000 0.146 0.094
## .Im18 0.482 0.046 10.494 0.000 0.482 0.247
## .Im9 1.415 0.089 15.908 0.000 1.415 0.776
## DECO 1.527 0.107 14.308 0.000 1.000 1.000
## FRENCH 0.412 0.064 6.422 0.000 1.000 1.000
## ATMOS 1.608 0.138 11.683 0.000 1.000 1.000
## QUAL 0.494 0.067 7.365 0.000 1.000 1.000
## CHOICE 1.518 0.110 13.746 0.000 1.000 1.000
## BRAND 1.402 0.100 14.036 0.000 1.000 1.000
Chi square: p-value > 0.05
RMSEA RMSEA <= 0.05 Good fit 0.05 < RMSEA <= 0.08 Acceptable fit 0.08 < RMSEA <= 0.10 Bad fit RMSEA > 0.1 Unacceptable fit
CFI CFI < 0.90 definitely reject model 0.90 < CFI < 0.95 high underrejection rates for misspecified models CFI > 0.95 accept model
# semPaths(CFA_fit_img_6f, what = "path", whatLabels = "std", style = "mx",
# rotation = 2, layout = "tree3", mar = c(1, 2, 1, 2),
# nCharNodes = 7,shapeMan = "rectangle", sizeMan = 8, sizeMan2 = 5,
# curvePivot=TRUE, edge.label.cex = 1.2, edge.color = "skyblue4")
semPaths(CFA_fit_img_6f, what = "path", whatLabels = "std", style = "mx",
rotation = 2, layout = "tree3", mar = c(1, 2, 1, 2),
nCharNodes = 7,shapeMan = "rectangle",
sizeMan = 4, sizeMan2 = 3, sizeInt = 2, sizeLat = 6, asize = 1.5,
curvePivot=TRUE, edge.label.cex = .8, edge.color = "skyblue4"
)lambda = inspect(CFA_fit_img_6f, what="std")$lambda
theta = inspect(CFA_fit_img_6f, what="std")$theta
# create lambda matrix with ones instead of std.all
ones <- lambda
ones[ones>0] <- 1
# a matrix with dimensions of lambda matrix but with lambdas replaced by thetas
theta_lb <- theta %*% ones# calculate indicator reliabilities (should be larger than 0.4)
indicrel <- lambda^2/(lambda^2 + theta_lb)
# indicrel
# replace all values satisfying condition with NaN for visibility
indicrel_fail <- indicrel
indicrel_fail[indicrel_fail>.4] <- NaN
indicrel_fail## DECO FRENCH ATMOS QUAL CHOICE BRAND
## Im3 NaN NaN NaN NaN NaN NaN
## Im4 NaN NaN NaN NaN NaN NaN
## Im5 NaN NaN NaN NaN NaN NaN
## Im6 NaN 0.286 NaN NaN NaN NaN
## Im7 NaN NaN NaN NaN NaN NaN
## Im8 NaN NaN NaN NaN NaN NaN
## Im10 NaN NaN NaN NaN NaN NaN
## Im14 NaN NaN NaN NaN NaN NaN
## Im20 NaN NaN NaN NaN NaN NaN
## Im21 NaN NaN NaN NaN NaN NaN
## Im22 NaN NaN NaN NaN NaN NaN
## Im11 NaN NaN NaN 0.378 NaN NaN
## Im12 NaN NaN NaN NaN NaN NaN
## Im13 NaN NaN NaN NaN NaN NaN
## Im1 NaN NaN NaN NaN NaN NaN
## Im2 NaN NaN NaN NaN NaN NaN
## Im15 NaN NaN NaN NaN NaN NaN
## Im16 NaN NaN NaN NaN 0.336 NaN
## Im19 NaN NaN NaN NaN 0.351 NaN
## Im17 NaN NaN NaN NaN NaN NaN
## Im18 NaN NaN NaN NaN NaN NaN
## Im9 NaN NaN NaN NaN NaN 0.224
# calculate construct reliability (should be above .6)
constrrel <- (t(lambda) %*% ones)^2 / ((t(lambda) %*% ones)^2 + t(theta_lb) %*% ones )
# constrrel
# replace all values satisfying condition with NaN for visibility
constrrel_fail <- constrrel
constrrel_fail[constrrel_fail>.6] <- NaN
constrrel_fail## DECO FRENCH ATMOS QUAL CHOICE BRAND
## DECO NaN NaN NaN NaN NaN NaN
## FRENCH NaN NaN NaN NaN NaN NaN
## ATMOS NaN NaN NaN NaN NaN NaN
## QUAL NaN NaN NaN NaN NaN NaN
## CHOICE NaN NaN NaN NaN NaN NaN
## BRAND NaN NaN NaN NaN NaN NaN
# calculate Average Variance Extracted (should be above .5)
AVE <- (t(lambda) %*% lambda) / (t(lambda) %*% lambda + t(theta_lb) %*% ones )
# avgvar
# replace all values satisfying condition with NaN for visibility
AVE_fail <- AVE
AVE_fail[AVE_fail>.5] <- NaN
AVE_fail## DECO FRENCH ATMOS QUAL CHOICE BRAND
## DECO NaN NaN NaN NaN NaN NaN
## FRENCH NaN NaN NaN NaN NaN NaN
## ATMOS NaN NaN NaN NaN NaN NaN
## QUAL NaN NaN NaN NaN NaN NaN
## CHOICE NaN NaN NaN NaN NaN NaN
## BRAND NaN NaN NaN NaN NaN NaN
# correlations between constructs (factors...) should be lower than .7
psi = inspect(CFA_fit_img_6f, what="std")$psi
psi_fail <- psi
psi_fail[psi_fail<.7] <- NaN
psi_fail## DECO FRENCH ATMOS QUAL CHOICE BRAND
## DECO 1
## FRENCH NaN 1
## ATMOS NaN NaN 1
## QUAL NaN NaN NaN 1
## CHOICE NaN NaN NaN NaN 1
## BRAND NaN NaN NaN NaN NaN 1
# AVE should be higher than squared correlations between constructs
# replace diagonal of psi matrix with AVE values
psi2 <- psi - psi * diag(1,nrow(psi),ncol(psi)) + diag(AVE) * diag(1,nrow(AVE),ncol(AVE))
# create matrix with columns filled with AVE
AVE_full <- AVE
AVE_full[is.na(AVE_full)] <- 0 #replace NAs with 0s
AVE_full <- AVE_full^0 %*% AVE_full # multiply a matrix full of ones with AVE_full to get columns filled with AVE
# substract matrices any psi bigger than AVE will be negative
AVEpsi_fail <- AVE_full - psi2
# AVE_full - psi2
AVEpsi_fail[AVEpsi_fail >= 0] <- NaN
AVE_full## DECO FRENCH ATMOS QUAL CHOICE BRAND
## DECO 0.7988422 0.5938271 0.6992777 0.6229362 0.5808676 0.6278343
## FRENCH 0.7988422 0.5938271 0.6992777 0.6229362 0.5808676 0.6278343
## ATMOS 0.7988422 0.5938271 0.6992777 0.6229362 0.5808676 0.6278343
## QUAL 0.7988422 0.5938271 0.6992777 0.6229362 0.5808676 0.6278343
## CHOICE 0.7988422 0.5938271 0.6992777 0.6229362 0.5808676 0.6278343
## BRAND 0.7988422 0.5938271 0.6992777 0.6229362 0.5808676 0.6278343
psi## DECO FRENCH ATMOS QUAL CHOICE BRAND
## DECO 1.000
## FRENCH 0.434 1.000
## ATMOS 0.466 0.326 1.000
## QUAL 0.471 0.456 0.419 1.000
## CHOICE 0.514 0.378 0.491 0.531 1.000
## BRAND 0.531 0.364 0.528 0.581 0.592 1.000
AVEpsi_fail## DECO FRENCH ATMOS QUAL CHOICE BRAND
## DECO .
## FRENCH NaN .
## ATMOS NaN NaN .
## QUAL NaN NaN NaN .
## CHOICE NaN NaN NaN NaN .
## BRAND NaN NaN NaN NaN -0.011 .
arrange(modificationindices(CFA_fit_img_6f),-mi)## lhs op rhs mi epc sepc.lv sepc.all sepc.nox
## 1 Im1 ~~ Im2 495.934 0.951 0.951 3.408 3.408
## 2 Im10 ~~ Im14 298.631 0.357 0.357 3.154 3.154
## 3 Im6 ~~ Im7 255.917 0.693 0.693 0.734 0.734
## 4 Im16 ~~ Im19 128.231 0.463 0.463 0.519 0.519
## 5 Im7 ~~ Im8 104.366 0.316 0.316 0.489 0.489
## 6 DECO =~ Im19 76.462 0.344 0.424 0.378 0.378
## 7 FRENCH =~ Im9 73.482 0.783 0.503 0.372 0.372
## 8 Im6 ~~ Im10 55.895 -0.158 -0.158 -0.438 -0.438
## 9 Im1 ~~ Im16 55.410 -0.242 -0.242 -0.489 -0.489
## 10 QUAL =~ Im15 54.596 0.510 0.359 0.299 0.299
## 11 Im6 ~~ Im8 52.130 0.236 0.236 0.335 0.335
## 12 Im7 ~~ Im14 50.063 -0.145 -0.145 -0.491 -0.491
## 13 FRENCH =~ Im19 49.872 0.497 0.319 0.284 0.284
## 14 Im15 ~~ Im16 49.062 0.263 0.263 0.332 0.332
## 15 Im1 ~~ Im19 46.763 -0.204 -0.204 -0.449 -0.449
## 16 QUAL =~ Im9 45.834 0.702 0.494 0.365 0.365
## 17 Im2 ~~ Im19 45.384 -0.198 -0.198 -0.393 -0.393
## 18 Im7 ~~ Im9 45.214 0.340 0.340 0.307 0.307
## 19 DECO =~ Im16 44.633 0.288 0.356 0.295 0.295
## 20 BRAND =~ Im19 43.739 0.300 0.355 0.316 0.316
## 21 Im7 ~~ Im10 41.088 -0.134 -0.134 -0.406 -0.406
## 22 QUAL =~ Im2 38.006 -0.361 -0.254 -0.197 -0.197
## 23 BRAND =~ Im15 37.135 0.254 0.301 0.251 0.251
## 24 Im17 ~~ Im18 36.588 0.762 0.762 2.870 2.870
## 25 Im2 ~~ Im15 35.103 -0.179 -0.179 -0.399 -0.399
## 26 Im15 ~~ Im19 34.736 0.202 0.202 0.277 0.277
## 27 QUAL =~ Im19 33.294 0.434 0.305 0.271 0.271
## 28 Im8 ~~ Im14 32.038 -0.103 -0.103 -0.467 -0.467
## 29 Im6 ~~ Im9 31.342 0.301 0.301 0.249 0.249
## 30 Im1 ~~ Im15 30.586 -0.174 -0.174 -0.429 -0.429
## 31 Im2 ~~ Im16 28.333 -0.170 -0.170 -0.311 -0.311
## 32 DECO =~ Im15 27.803 0.191 0.236 0.197 0.197
## 33 Im6 ~~ Im14 27.360 -0.108 -0.108 -0.335 -0.335
## 34 FRENCH =~ Im16 27.263 0.403 0.259 0.214 0.214
## 35 DECO =~ Im2 26.666 -0.158 -0.195 -0.152 -0.152
## 36 ATMOS =~ Im15 24.669 0.181 0.230 0.192 0.192
## 37 BRAND =~ Im13 23.589 0.232 0.275 0.228 0.228
## 38 DECO =~ Im1 22.892 -0.149 -0.184 -0.138 -0.138
## 39 ATMOS =~ Im2 21.308 -0.142 -0.180 -0.140 -0.140
## 40 Im11 ~~ Im13 21.300 -0.191 -0.191 -0.339 -0.339
## 41 BRAND =~ Im2 21.047 -0.165 -0.195 -0.152 -0.152
## 42 FRENCH =~ Im1 20.125 -0.244 -0.156 -0.118 -0.118
## 43 FRENCH =~ Im15 18.582 0.279 0.179 0.149 0.149
## 44 BRAND =~ Im12 18.526 -0.197 -0.233 -0.205 -0.205
## 45 BRAND =~ Im16 17.630 0.209 0.247 0.205 0.205
## 46 BRAND =~ Im1 16.671 -0.150 -0.177 -0.133 -0.133
## 47 ATMOS =~ Im19 16.384 0.161 0.204 0.181 0.181
## 48 BRAND =~ Im6 14.589 0.161 0.191 0.159 0.159
## 49 CHOICE =~ Im20 14.430 -0.169 -0.208 -0.139 -0.139
## 50 Im14 ~~ Im9 13.864 -0.082 -0.082 -0.217 -0.217
## 51 Im11 ~~ Im12 13.374 0.145 0.145 0.289 0.289
## 52 Im21 ~~ Im22 13.217 -0.270 -0.270 -0.427 -0.427
## 53 CHOICE =~ Im13 13.044 0.152 0.187 0.155 0.155
## 54 ATMOS =~ Im7 12.806 0.134 0.170 0.140 0.140
## 55 Im8 ~~ Im10 12.666 -0.065 -0.065 -0.265 -0.265
## 56 FRENCH =~ Im11 12.345 0.269 0.173 0.151 0.151
## 57 CHOICE =~ Im12 11.541 -0.136 -0.168 -0.148 -0.148
## 58 Im3 ~~ Im4 11.447 0.264 0.264 1.735 1.735
## 59 ATMOS =~ Im16 11.243 0.146 0.185 0.153 0.153
## 60 ATMOS =~ Im12 11.072 -0.115 -0.146 -0.128 -0.128
## 61 Im8 ~~ Im9 10.943 0.125 0.125 0.152 0.152
## 62 FRENCH =~ Im2 10.891 -0.177 -0.114 -0.088 -0.088
## 63 Im7 ~~ Im22 10.253 0.126 0.126 0.182 0.182
## 64 DECO =~ Im9 10.194 0.167 0.207 0.153 0.153
## 65 Im11 ~~ Im9 10.067 0.156 0.156 0.145 0.145
## 66 Im15 ~~ Im9 9.926 0.139 0.139 0.145 0.145
## 67 QUAL =~ Im16 9.231 0.250 0.176 0.146 0.146
## 68 Im8 ~~ Im15 9.159 0.080 0.080 0.144 0.144
## 69 ATMOS =~ Im9 9.070 0.162 0.205 0.152 0.152
## 70 Im13 ~~ Im17 9.051 0.067 0.067 0.281 0.281
## 71 Im6 ~~ Im22 8.985 0.125 0.125 0.166 0.166
## 72 Im20 ~~ Im21 8.930 0.206 0.206 0.306 0.306
## 73 BRAND =~ Im22 8.880 0.147 0.175 0.114 0.114
## 74 Im8 ~~ Im16 8.801 0.095 0.095 0.139 0.139
## 75 BRAND =~ Im20 8.486 -0.141 -0.167 -0.111 -0.111
## 76 BRAND =~ Im7 8.244 0.114 0.135 0.111 0.111
## 77 Im3 ~~ Im1 8.143 -0.045 -0.045 -0.194 -0.194
## 78 Im8 ~~ Im2 7.823 -0.059 -0.059 -0.153 -0.153
## 79 QUAL =~ Im18 7.388 -0.230 -0.161 -0.115 -0.115
## 80 Im10 ~~ Im16 7.338 0.052 0.052 0.149 0.149
## 81 Im13 ~~ Im1 7.263 0.060 0.060 0.191 0.191
## 82 Im4 ~~ Im17 7.109 -0.041 -0.041 -0.322 -0.322
## 83 Im22 ~~ Im12 7.028 -0.078 -0.078 -0.189 -0.189
## 84 Im17 ~~ Im9 7.005 -0.112 -0.112 -0.247 -0.247
## 85 DECO =~ Im6 6.969 0.109 0.134 0.112 0.112
## 86 ATMOS =~ Im11 6.857 0.102 0.130 0.113 0.113
## 87 CHOICE =~ Im9 6.692 0.148 0.182 0.135 0.135
## 88 ATMOS =~ Im6 6.616 0.102 0.130 0.108 0.108
## 89 Im14 ~~ Im2 6.285 0.031 0.031 0.175 0.175
## 90 BRAND =~ Im5 6.246 0.103 0.122 0.092 0.092
## 91 BRAND =~ Im4 6.180 -0.071 -0.084 -0.062 -0.062
## 92 Im22 ~~ Im9 5.999 0.121 0.121 0.136 0.136
## 93 QUAL =~ Im5 5.978 0.169 0.119 0.089 0.089
## 94 Im1 ~~ Im9 5.822 -0.084 -0.084 -0.140 -0.140
## 95 QUAL =~ Im1 5.747 -0.143 -0.100 -0.075 -0.075
## 96 CHOICE =~ Im18 5.737 -0.115 -0.141 -0.101 -0.101
## 97 Im3 ~~ Im5 5.693 -0.084 -0.084 -0.209 -0.209
## 98 Im8 ~~ Im22 5.661 0.070 0.070 0.136 0.136
## 99 DECO =~ Im20 5.578 -0.100 -0.123 -0.082 -0.082
## 100 ATMOS =~ Im5 5.473 0.089 0.112 0.084 0.084
## 101 DECO =~ Im17 5.404 -0.091 -0.112 -0.090 -0.090
## 102 Im11 ~~ Im17 5.351 -0.061 -0.061 -0.177 -0.177
## 103 CHOICE =~ Im5 5.052 0.088 0.108 0.082 0.082
## 104 FRENCH =~ Im13 4.802 -0.157 -0.101 -0.084 -0.084
## 105 DECO =~ Im22 4.756 0.094 0.116 0.076 0.076
## 106 Im22 ~~ Im11 4.722 0.083 0.083 0.124 0.124
## 107 CHOICE =~ Im22 4.719 0.099 0.122 0.080 0.080
## 108 Im13 ~~ Im16 4.625 -0.073 -0.073 -0.118 -0.118
## 109 Im19 ~~ Im17 4.621 0.056 0.056 0.161 0.161
## 110 ATMOS =~ Im10 4.609 -0.038 -0.048 -0.055 -0.055
## 111 BRAND =~ Im10 4.570 -0.040 -0.048 -0.054 -0.054
## 112 Im14 ~~ Im22 4.494 -0.036 -0.036 -0.154 -0.154
## 113 ATMOS =~ Im4 4.422 -0.053 -0.067 -0.050 -0.050
## 114 Im14 ~~ Im15 4.415 -0.032 -0.032 -0.127 -0.127
## 115 Im21 ~~ Im9 4.370 -0.102 -0.102 -0.101 -0.101
## 116 Im10 ~~ Im13 4.362 -0.031 -0.031 -0.138 -0.138
## 117 Im7 ~~ Im15 4.358 0.074 0.074 0.098 0.098
## 118 Im3 ~~ Im22 4.300 0.047 0.047 0.135 0.135
## 119 Im20 ~~ Im1 4.283 -0.056 -0.056 -0.141 -0.141
## 120 Im4 ~~ Im16 4.262 0.048 0.048 0.149 0.149
## 121 FRENCH =~ Im5 4.167 0.144 0.093 0.070 0.070
## 122 ATMOS =~ Im8 4.061 0.057 0.072 0.068 0.068
## 123 Im6 ~~ Im20 4.039 -0.084 -0.084 -0.105 -0.105
## 124 Im10 ~~ Im11 4.002 0.036 0.036 0.111 0.111
## 125 Im20 ~~ Im17 3.990 -0.054 -0.054 -0.177 -0.177
## 126 Im6 ~~ Im11 3.977 -0.083 -0.083 -0.091 -0.091
## 127 Im5 ~~ Im1 3.869 0.051 0.051 0.117 0.117
## 128 Im15 ~~ Im17 3.695 0.045 0.045 0.147 0.147
## 129 Im4 ~~ Im18 3.604 0.035 0.035 0.152 0.152
## 130 Im12 ~~ Im15 3.556 0.050 0.050 0.110 0.110
## 131 FRENCH =~ Im17 3.536 -0.115 -0.074 -0.060 -0.060
## 132 Im14 ~~ Im16 3.474 -0.035 -0.035 -0.110 -0.110
## 133 Im3 ~~ Im15 3.381 0.037 0.037 0.099 0.099
## 134 Im3 ~~ Im17 3.375 0.029 0.029 0.161 0.161
## 135 Im3 ~~ Im19 3.371 0.040 0.040 0.096 0.096
## 136 Im13 ~~ Im15 3.338 0.051 0.051 0.102 0.102
## 137 Im22 ~~ Im1 3.275 0.049 0.049 0.132 0.132
## 138 Im20 ~~ Im13 3.270 0.057 0.057 0.115 0.115
## 139 Im13 ~~ Im2 3.219 -0.040 -0.040 -0.116 -0.116
## 140 Im11 ~~ Im1 3.071 -0.047 -0.047 -0.104 -0.104
## 141 CHOICE =~ Im21 3.048 0.074 0.091 0.066 0.066
## 142 Im10 ~~ Im17 3.000 -0.021 -0.021 -0.157 -0.157
## 143 ATMOS =~ Im1 2.962 -0.054 -0.068 -0.051 -0.051
## 144 ATMOS =~ Im13 2.889 0.062 0.078 0.065 0.065
## 145 Im16 ~~ Im9 2.810 0.089 0.089 0.076 0.076
## 146 Im5 ~~ Im14 2.794 0.028 0.028 0.101 0.101
## 147 Im4 ~~ Im22 2.701 -0.036 -0.036 -0.146 -0.146
## 148 CHOICE =~ Im10 2.670 -0.030 -0.037 -0.042 -0.042
## 149 Im1 ~~ Im17 2.662 -0.031 -0.031 -0.161 -0.161
## 150 ATMOS =~ Im14 2.649 -0.028 -0.035 -0.041 -0.041
## 151 Im4 ~~ Im19 2.526 0.034 0.034 0.113 0.113
## 152 Im4 ~~ Im11 2.492 -0.034 -0.034 -0.115 -0.115
## 153 Im21 ~~ Im18 2.456 -0.050 -0.050 -0.086 -0.086
## 154 Im12 ~~ Im2 2.343 -0.032 -0.032 -0.104 -0.104
## 155 Im6 ~~ Im15 2.316 0.057 0.057 0.070 0.070
## 156 Im12 ~~ Im9 2.302 0.057 0.057 0.086 0.086
## 157 DECO =~ Im12 2.287 -0.054 -0.067 -0.059 -0.059
## 158 Im6 ~~ Im1 2.248 -0.044 -0.044 -0.087 -0.087
## 159 Im3 ~~ Im20 2.237 -0.034 -0.034 -0.091 -0.091
## 160 Im15 ~~ Im18 2.236 -0.043 -0.043 -0.077 -0.077
## 161 Im7 ~~ Im1 2.236 -0.042 -0.042 -0.089 -0.089
## 162 Im6 ~~ Im12 2.164 -0.047 -0.047 -0.083 -0.083
## 163 Im10 ~~ Im12 2.160 0.020 0.020 0.102 0.102
## 164 Im4 ~~ Im2 2.090 -0.022 -0.022 -0.123 -0.123
## 165 Im5 ~~ Im6 1.873 -0.055 -0.055 -0.063 -0.063
## 166 Im4 ~~ Im6 1.846 0.032 0.032 0.096 0.096
## 167 DECO =~ Im10 1.832 -0.025 -0.031 -0.035 -0.035
## 168 Im22 ~~ Im2 1.825 -0.037 -0.037 -0.090 -0.090
## 169 Im10 ~~ Im22 1.781 -0.024 -0.024 -0.090 -0.090
## 170 Im12 ~~ Im17 1.776 -0.028 -0.028 -0.131 -0.131
## 171 Im6 ~~ Im18 1.754 0.047 0.047 0.066 0.066
## 172 Im21 ~~ Im17 1.749 0.035 0.035 0.108 0.108
## 173 Im5 ~~ Im16 1.746 -0.052 -0.052 -0.062 -0.062
## 174 Im3 ~~ Im12 1.732 -0.023 -0.023 -0.087 -0.087
## 175 Im22 ~~ Im13 1.726 -0.041 -0.041 -0.089 -0.089
## 176 Im18 ~~ Im9 1.696 -0.060 -0.060 -0.073 -0.073
## 177 ATMOS =~ Im17 1.682 -0.052 -0.065 -0.053 -0.053
## 178 QUAL =~ Im4 1.672 -0.060 -0.042 -0.031 -0.031
## 179 Im20 ~~ Im19 1.649 0.048 0.048 0.067 0.067
## 180 Im20 ~~ Im2 1.631 -0.035 -0.035 -0.080 -0.080
## 181 FRENCH =~ Im18 1.599 -0.082 -0.052 -0.038 -0.038
## 182 Im4 ~~ Im12 1.546 0.021 0.021 0.113 0.113
## 183 CHOICE =~ Im17 1.544 0.057 0.071 0.057 0.057
## 184 Im6 ~~ Im19 1.483 0.050 0.050 0.055 0.055
## 185 Im12 ~~ Im16 1.481 0.038 0.038 0.070 0.070
## 186 Im7 ~~ Im16 1.479 -0.052 -0.052 -0.056 -0.056
## 187 DECO =~ Im13 1.462 0.045 0.056 0.046 0.046
## 188 FRENCH =~ Im20 1.442 -0.089 -0.057 -0.038 -0.038
## 189 Im12 ~~ Im13 1.442 0.089 0.089 0.255 0.255
## 190 BRAND =~ Im3 1.434 0.033 0.039 0.030 0.030
## 191 Im12 ~~ Im1 1.360 -0.024 -0.024 -0.087 -0.087
## 192 Im3 ~~ Im18 1.301 -0.022 -0.022 -0.067 -0.067
## 193 Im16 ~~ Im17 1.269 0.032 0.032 0.085 0.085
## 194 Im3 ~~ Im11 1.261 0.025 0.025 0.060 0.060
## 195 Im14 ~~ Im17 1.252 0.013 0.013 0.110 0.110
## 196 Im10 ~~ Im19 1.233 0.019 0.019 0.060 0.060
## 197 Im3 ~~ Im10 1.230 0.012 0.012 0.070 0.070
## 198 Im8 ~~ Im18 1.200 -0.027 -0.027 -0.057 -0.057
## 199 Im8 ~~ Im1 1.194 -0.023 -0.023 -0.065 -0.065
## 200 Im21 ~~ Im2 1.185 0.030 0.030 0.063 0.063
## 201 QUAL =~ Im22 1.168 -0.084 -0.059 -0.038 -0.038
## 202 CHOICE =~ Im14 1.154 0.019 0.023 0.027 0.027
## 203 Im10 ~~ Im9 1.119 0.024 0.024 0.057 0.057
## 204 DECO =~ Im18 1.115 0.043 0.053 0.038 0.038
## 205 CHOICE =~ Im4 1.111 -0.028 -0.035 -0.026 -0.026
## 206 Im14 ~~ Im21 1.104 0.018 0.018 0.067 0.067
## 207 Im5 ~~ Im19 1.093 -0.038 -0.038 -0.048 -0.048
## 208 Im4 ~~ Im8 1.089 0.017 0.017 0.076 0.076
## 209 Im22 ~~ Im18 1.078 0.034 0.034 0.065 0.065
## 210 Im22 ~~ Im15 1.067 0.036 0.036 0.059 0.059
## 211 Im13 ~~ Im18 1.031 -0.027 -0.027 -0.062 -0.062
## 212 CHOICE =~ Im7 0.941 0.037 0.046 0.038 0.038
## 213 Im4 ~~ Im10 0.906 -0.010 -0.010 -0.082 -0.082
## 214 Im3 ~~ Im14 0.890 -0.010 -0.010 -0.065 -0.065
## 215 Im10 ~~ Im2 0.889 -0.012 -0.012 -0.061 -0.061
## 216 ATMOS =~ Im3 0.869 0.023 0.029 0.022 0.022
## 217 Im11 ~~ Im16 0.846 0.038 0.038 0.043 0.043
## 218 QUAL =~ Im14 0.840 0.031 0.022 0.026 0.026
## 219 QUAL =~ Im20 0.837 0.069 0.049 0.033 0.033
## 220 Im1 ~~ Im18 0.830 0.021 0.021 0.060 0.060
## 221 Im3 ~~ Im16 0.818 0.022 0.022 0.048 0.048
## 222 DECO =~ Im7 0.814 0.035 0.043 0.036 0.036
## 223 Im2 ~~ Im18 0.811 -0.021 -0.021 -0.054 -0.054
## 224 Im20 ~~ Im12 0.794 0.026 0.026 0.059 0.059
## 225 FRENCH =~ Im22 0.781 0.067 0.043 0.028 0.028
## 226 Im20 ~~ Im16 0.767 0.036 0.036 0.046 0.046
## 227 Im14 ~~ Im18 0.739 -0.012 -0.012 -0.056 -0.056
## 228 Im22 ~~ Im19 0.717 -0.032 -0.032 -0.047 -0.047
## 229 QUAL =~ Im10 0.654 -0.028 -0.020 -0.023 -0.023
## 230 Im14 ~~ Im13 0.649 0.011 0.011 0.057 0.057
## 231 Im14 ~~ Im11 0.639 0.014 0.014 0.048 0.048
## 232 CHOICE =~ Im6 0.612 0.032 0.039 0.033 0.033
## 233 Im19 ~~ Im9 0.595 0.037 0.037 0.035 0.035
## 234 BRAND =~ Im11 0.591 -0.036 -0.043 -0.038 -0.038
## 235 Im6 ~~ Im2 0.577 -0.023 -0.023 -0.040 -0.040
## 236 Im20 ~~ Im15 0.576 0.026 0.026 0.041 0.041
## 237 Im5 ~~ Im22 0.561 0.027 0.027 0.043 0.043
## 238 Im8 ~~ Im19 0.558 0.022 0.022 0.035 0.035
## 239 Im8 ~~ Im21 0.538 -0.022 -0.022 -0.037 -0.037
## 240 Im21 ~~ Im12 0.537 0.021 0.021 0.045 0.045
## 241 Im11 ~~ Im19 0.536 0.028 0.028 0.034 0.034
## 242 Im21 ~~ Im1 0.534 0.020 0.020 0.046 0.046
## 243 QUAL =~ Im7 0.517 0.053 0.037 0.031 0.031
## 244 Im10 ~~ Im18 0.516 0.011 0.011 0.044 0.044
## 245 Im5 ~~ Im11 0.511 0.026 0.026 0.034 0.034
## 246 Im10 ~~ Im20 0.483 0.012 0.012 0.044 0.044
## 247 Im12 ~~ Im18 0.465 -0.017 -0.017 -0.044 -0.044
## 248 Im14 ~~ Im1 0.460 0.008 0.008 0.052 0.052
## 249 FRENCH =~ Im3 0.457 -0.031 -0.020 -0.015 -0.015
## 250 Im20 ~~ Im11 0.453 0.026 0.026 0.036 0.036
## 251 Im3 ~~ Im8 0.442 -0.012 -0.012 -0.036 -0.036
## 252 Im20 ~~ Im18 0.417 0.021 0.021 0.038 0.038
## 253 Im20 ~~ Im22 0.407 0.061 0.061 0.103 0.103
## 254 Im10 ~~ Im1 0.405 -0.008 -0.008 -0.045 -0.045
## 255 Im5 ~~ Im20 0.402 0.023 0.023 0.034 0.034
## 256 BRAND =~ Im14 0.390 -0.011 -0.014 -0.016 -0.016
## 257 Im2 ~~ Im9 0.381 -0.022 -0.022 -0.033 -0.033
## 258 Im21 ~~ Im11 0.373 -0.023 -0.023 -0.030 -0.030
## 259 Im16 ~~ Im18 0.357 -0.021 -0.021 -0.030 -0.030
## 260 Im5 ~~ Im15 0.339 -0.019 -0.019 -0.028 -0.028
## 261 Im21 ~~ Im13 0.328 -0.018 -0.018 -0.034 -0.034
## 262 QUAL =~ Im8 0.320 -0.031 -0.022 -0.021 -0.021
## 263 Im5 ~~ Im21 0.319 -0.021 -0.021 -0.028 -0.028
## 264 DECO =~ Im8 0.317 0.016 0.020 0.019 0.019
## 265 Im7 ~~ Im19 0.317 0.022 0.022 0.026 0.026
## 266 Im4 ~~ Im20 0.315 0.012 0.012 0.047 0.047
## 267 Im11 ~~ Im2 0.310 0.015 0.015 0.030 0.030
## 268 Im5 ~~ Im8 0.298 -0.015 -0.015 -0.026 -0.026
## 269 Im7 ~~ Im20 0.292 -0.021 -0.021 -0.029 -0.029
## 270 Im4 ~~ Im13 0.275 -0.009 -0.009 -0.045 -0.045
## 271 Im3 ~~ Im13 0.274 0.010 0.010 0.033 0.033
## 272 Im8 ~~ Im13 0.252 -0.012 -0.012 -0.028 -0.028
## 273 DECO =~ Im11 0.240 0.019 0.024 0.021 0.021
## 274 Im12 ~~ Im19 0.218 0.013 0.013 0.027 0.027
## 275 Im4 ~~ Im5 0.193 0.017 0.017 0.059 0.059
## 276 Im3 ~~ Im7 0.193 -0.010 -0.010 -0.024 -0.024
## 277 Im7 ~~ Im12 0.191 -0.013 -0.013 -0.025 -0.025
## 278 Im5 ~~ Im17 0.190 0.011 0.011 0.033 0.033
## 279 Im7 ~~ Im21 0.188 -0.017 -0.017 -0.022 -0.022
## 280 Im5 ~~ Im9 0.179 0.020 0.020 0.019 0.019
## 281 Im19 ~~ Im18 0.174 -0.013 -0.013 -0.021 -0.021
## 282 Im21 ~~ Im16 0.170 -0.017 -0.017 -0.020 -0.020
## 283 FRENCH =~ Im4 0.152 -0.018 -0.012 -0.009 -0.009
## 284 Im4 ~~ Im15 0.151 -0.008 -0.008 -0.028 -0.028
## 285 Im21 ~~ Im19 0.149 -0.014 -0.014 -0.019 -0.019
## 286 DECO =~ Im14 0.132 -0.007 -0.008 -0.009 -0.009
## 287 Im4 ~~ Im1 0.125 0.005 0.005 0.033 0.033
## 288 Im3 ~~ Im2 0.124 0.006 0.006 0.022 0.022
## 289 Im2 ~~ Im17 0.116 0.006 0.006 0.031 0.031
## 290 Im10 ~~ Im15 0.108 -0.005 -0.005 -0.018 -0.018
## 291 Im5 ~~ Im10 0.106 -0.006 -0.006 -0.018 -0.018
## 292 FRENCH =~ Im21 0.106 0.023 0.015 0.011 0.011
## 293 Im6 ~~ Im16 0.097 -0.014 -0.014 -0.014 -0.014
## 294 CHOICE =~ Im8 0.094 -0.009 -0.011 -0.010 -0.010
## 295 Im7 ~~ Im11 0.091 -0.012 -0.012 -0.014 -0.014
## 296 Im10 ~~ Im21 0.089 -0.005 -0.005 -0.018 -0.018
## 297 Im11 ~~ Im18 0.089 0.010 0.010 0.015 0.015
## 298 Im5 ~~ Im2 0.087 -0.008 -0.008 -0.016 -0.016
## 299 Im7 ~~ Im18 0.086 -0.010 -0.010 -0.015 -0.015
## 300 QUAL =~ Im6 0.086 -0.023 -0.016 -0.013 -0.013
## 301 Im5 ~~ Im12 0.084 0.008 0.008 0.017 0.017
## 302 CHOICE =~ Im11 0.082 -0.012 -0.015 -0.013 -0.013
## 303 Im8 ~~ Im12 0.076 -0.006 -0.006 -0.016 -0.016
## 304 Im6 ~~ Im13 0.071 0.009 0.009 0.014 0.014
## 305 Im14 ~~ Im20 0.068 -0.004 -0.004 -0.018 -0.018
## 306 Im5 ~~ Im7 0.064 0.010 0.010 0.012 0.012
## 307 Im22 ~~ Im17 0.054 0.006 0.006 0.022 0.022
## 308 Im6 ~~ Im21 0.052 -0.010 -0.010 -0.011 -0.011
## 309 QUAL =~ Im21 0.051 0.016 0.011 0.008 0.008
## 310 Im4 ~~ Im21 0.046 0.005 0.005 0.017 0.017
## 311 Im21 ~~ Im15 0.040 -0.007 -0.007 -0.010 -0.010
## 312 Im14 ~~ Im12 0.039 -0.003 -0.003 -0.015 -0.015
## 313 Im7 ~~ Im13 0.037 -0.006 -0.006 -0.011 -0.011
## 314 Im8 ~~ Im17 0.036 -0.004 -0.004 -0.015 -0.015
## 315 QUAL =~ Im17 0.035 -0.015 -0.011 -0.009 -0.009
## 316 BRAND =~ Im21 0.027 -0.007 -0.009 -0.006 -0.006
## 317 Im14 ~~ Im19 0.027 0.003 0.003 0.010 0.010
## 318 Im20 ~~ Im9 0.021 0.007 0.007 0.008 0.008
## 319 Im7 ~~ Im17 0.021 -0.004 -0.004 -0.011 -0.011
## 320 BRAND =~ Im8 0.020 0.004 0.005 0.005 0.005
## 321 CHOICE =~ Im3 0.018 -0.004 -0.004 -0.003 -0.003
## 322 Im3 ~~ Im9 0.018 -0.004 -0.004 -0.007 -0.007
## 323 Im5 ~~ Im18 0.017 0.004 0.004 0.007 0.007
## 324 DECO =~ Im21 0.017 0.005 0.006 0.005 0.005
## 325 Im8 ~~ Im20 0.014 0.003 0.003 0.006 0.006
## 326 Im4 ~~ Im9 0.014 -0.003 -0.003 -0.008 -0.008
## 327 Im3 ~~ Im21 0.010 -0.002 -0.002 -0.006 -0.006
## 328 ATMOS =~ Im18 0.009 0.004 0.005 0.004 0.004
## 329 Im11 ~~ Im15 0.007 -0.003 -0.003 -0.004 -0.004
## 330 Im7 ~~ Im2 0.006 -0.002 -0.002 -0.004 -0.004
## 331 FRENCH =~ Im12 0.002 -0.003 -0.002 -0.002 -0.002
## 332 Im13 ~~ Im9 0.002 0.002 0.002 0.003 0.003
## 333 Im4 ~~ Im14 0.002 0.000 0.000 -0.004 -0.004
## 334 Im4 ~~ Im7 0.002 -0.001 -0.001 -0.003 -0.003
## 335 Im8 ~~ Im11 0.002 0.001 0.001 0.002 0.002
## 336 Im13 ~~ Im19 0.002 0.001 0.001 0.002 0.002
## 337 Im3 ~~ Im6 0.002 0.001 0.001 0.002 0.002
## 338 Im22 ~~ Im16 0.001 0.001 0.001 0.002 0.002
## 339 QUAL =~ Im3 0.001 0.001 0.001 0.001 0.001
## 340 Im6 ~~ Im17 0.000 0.000 0.000 -0.001 -0.001
## 341 Im5 ~~ Im13 0.000 0.000 0.000 0.000 0.000
Based on the modification indices we create a new model
# # no excluded variables:
# CFA_model_img_7f <- "
# DECO =~ Im3 + Im4 + Im5
# FOOD =~ Im8 + Im10 + Im14
# ATMOS =~ Im20 + Im21 + Im22
# PRODQUAL =~ Im11 + Im12 + Im13
# CHOICE =~ Im1 + Im2 + Im15 + Im16 + Im19
# BRAND =~ Im17 + Im18
# FRENCH =~ Im6 + Im7 + Im9
# "
# MIs indicate separate Im1, Im2 and Im16, Im19 no excluded variables
# Im8 under FRENCH
# exclude Im8
# exclude Im15
# exclude Im9
CFA_model_img_7f <- "
DECO =~ Im3 + Im4 + Im5
FOOD =~ Im10 + Im14
ATMOS =~ Im20 + Im21 + Im22
PRODQUAL =~ Im11 + Im12 + Im13
CHOICE =~ Im1 + Im2
PROF =~ Im16 + Im19
BRAND =~ Im17 + Im18
FRENCH =~ Im6 + Im7
"
# # excluded variables: Im9, Im15, Im16, Im19
# CFA_model_img_7f <- "
# QUAL =~ Im11 + Im12 + Im13
# FOOD =~ Im8 + Im10 + Im14
# ATMOS =~ Im20 + Im21 + Im22
# DECO =~ Im3 + Im4 + Im5
# CHOICE =~ Im1 + Im2
# BRAND =~ Im17 + Im18
# FRENCH =~ Im6 + Im7
# "
# # excluded variables: Im9, Im15, Im16, Im19, Im8
# CFA_model_img_7f <- "
# QUAL =~ Im11 + Im12 + Im13
# FOOD =~ Im10 + Im14
# ATMOS =~ Im20 + Im21 + Im22
# DECO =~ Im3 + Im4 + Im5
# CHOICE =~ Im1 + Im2
# BRAND =~ Im17 + Im18
# FRENCH =~ Im6 + Im7
# "
# # 8 factor model: excluded variables: Im9, Im15, Im8, Im11
# CFA_model_img_7f <- "
# QUAL =~ Im12 + Im13
# FOOD =~ Im10 + Im14
# ATMOS =~ Im20 + Im21 + Im22
# DECO =~ Im3 + Im4 + Im5
# CHOICE =~ Im1 + Im2
# BRAND =~ Im17 + Im18
# FRENCH =~ Im6 + Im7
# PROF =~ Im16 + Im19
# "
CFA_fit_img_7f <- cfa(CFA_model_img_7f, data=survey, missing="ML")
summary(CFA_fit_img_7f, fit.measures=TRUE, standardized=TRUE)## lavaan 0.6.15 ended normally after 108 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 85
##
## Number of observations 553
## Number of missing patterns 79
##
## Model Test User Model:
##
## Test statistic 259.047
## Degrees of freedom 124
## P-value (Chi-square) 0.000
##
## Model Test Baseline Model:
##
## Test statistic 7474.765
## Degrees of freedom 171
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.982
## Tucker-Lewis Index (TLI) 0.975
##
## Robust Comparative Fit Index (CFI) 0.981
## Robust Tucker-Lewis Index (TLI) 0.974
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -12973.111
## Loglikelihood unrestricted model (H1) -12843.588
##
## Akaike (AIC) 26116.223
## Bayesian (BIC) 26483.028
## Sample-size adjusted Bayesian (SABIC) 26213.200
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.044
## 90 Percent confidence interval - lower 0.037
## 90 Percent confidence interval - upper 0.052
## P-value H_0: RMSEA <= 0.050 0.886
## P-value H_0: RMSEA >= 0.080 0.000
##
## Robust RMSEA 0.045
## 90 Percent confidence interval - lower 0.038
## 90 Percent confidence interval - upper 0.053
## P-value H_0: Robust RMSEA <= 0.050 0.825
## P-value H_0: Robust RMSEA >= 0.080 0.000
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.029
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Observed
## Observed information based on Hessian
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## DECO =~
## Im3 1.000 1.236 0.937
## Im4 1.056 0.025 42.717 0.000 1.305 0.969
## Im5 0.818 0.034 23.815 0.000 1.011 0.760
## FOOD =~
## Im10 1.000 0.812 0.923
## Im14 1.015 0.036 28.479 0.000 0.824 0.952
## ATMOS =~
## Im20 1.000 1.265 0.845
## Im21 0.849 0.041 20.823 0.000 1.074 0.783
## Im22 1.060 0.047 22.606 0.000 1.340 0.877
## PRODQUAL =~
## Im11 1.000 0.703 0.615
## Im12 1.410 0.094 15.046 0.000 0.991 0.872
## Im13 1.465 0.105 13.968 0.000 1.030 0.855
## CHOICE =~
## Im1 1.000 1.305 0.980
## Im2 0.885 0.033 27.043 0.000 1.155 0.899
## PROF =~
## Im16 1.000 0.921 0.766
## Im19 1.046 0.061 17.170 0.000 0.963 0.856
## BRAND =~
## Im17 1.000 1.204 0.969
## Im18 0.994 0.041 24.143 0.000 1.197 0.856
## FRENCH =~
## Im6 1.000 0.975 0.813
## Im7 1.184 0.071 16.770 0.000 1.155 0.955
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## DECO ~~
## FOOD 0.418 0.050 8.393 0.000 0.416 0.416
## ATMOS 0.730 0.082 8.912 0.000 0.467 0.467
## PRODQUAL 0.409 0.051 8.040 0.000 0.471 0.471
## CHOICE 0.711 0.079 9.032 0.000 0.441 0.441
## PROF 0.743 0.071 10.465 0.000 0.653 0.653
## BRAND 0.770 0.076 10.140 0.000 0.517 0.517
## FRENCH 0.402 0.063 6.350 0.000 0.334 0.334
## FOOD ~~
## ATMOS 0.303 0.051 5.948 0.000 0.295 0.295
## PRODQUAL 0.258 0.034 7.662 0.000 0.452 0.452
## CHOICE 0.328 0.050 6.584 0.000 0.309 0.309
## PROF 0.372 0.043 8.589 0.000 0.498 0.498
## BRAND 0.318 0.047 6.801 0.000 0.325 0.325
## FRENCH 0.463 0.047 9.829 0.000 0.585 0.585
## ATMOS ~~
## PRODQUAL 0.372 0.053 7.011 0.000 0.418 0.418
## CHOICE 0.739 0.085 8.728 0.000 0.448 0.448
## PROF 0.557 0.069 8.089 0.000 0.478 0.478
## BRAND 0.787 0.081 9.715 0.000 0.516 0.516
## FRENCH 0.410 0.065 6.352 0.000 0.333 0.333
## PRODQUAL ~~
## CHOICE 0.439 0.054 8.161 0.000 0.478 0.478
## PROF 0.343 0.043 7.946 0.000 0.529 0.529
## BRAND 0.479 0.053 9.046 0.000 0.566 0.566
## FRENCH 0.210 0.037 5.622 0.000 0.306 0.306
## CHOICE ~~
## PROF 0.717 0.072 9.956 0.000 0.597 0.597
## BRAND 0.817 0.079 10.362 0.000 0.519 0.519
## FRENCH 0.286 0.060 4.735 0.000 0.225 0.225
## PROF ~~
## BRAND 0.667 0.066 10.040 0.000 0.601 0.601
## FRENCH 0.328 0.051 6.438 0.000 0.366 0.366
## BRAND ~~
## FRENCH 0.378 0.061 6.175 0.000 0.322 0.322
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .Im3 4.995 0.056 88.560 0.000 4.995 3.786
## .Im4 4.999 0.057 86.983 0.000 4.999 3.712
## .Im5 5.035 0.057 87.844 0.000 5.035 3.787
## .Im10 6.100 0.037 162.789 0.000 6.100 6.937
## .Im14 6.138 0.037 165.861 0.000 6.138 7.093
## .Im20 4.672 0.064 73.177 0.000 4.672 3.123
## .Im21 5.139 0.058 87.970 0.000 5.139 3.751
## .Im22 4.279 0.065 65.401 0.000 4.279 2.799
## .Im11 5.653 0.049 115.271 0.000 5.653 4.943
## .Im12 5.666 0.049 116.089 0.000 5.666 4.983
## .Im13 5.448 0.052 105.615 0.000 5.448 4.524
## .Im1 4.790 0.057 84.202 0.000 4.790 3.597
## .Im2 4.857 0.055 88.354 0.000 4.857 3.779
## .Im16 5.135 0.052 99.147 0.000 5.135 4.269
## .Im19 5.145 0.048 106.948 0.000 5.145 4.574
## .Im17 5.025 0.053 94.519 0.000 5.025 4.041
## .Im18 4.595 0.060 76.447 0.000 4.595 3.287
## .Im6 5.827 0.051 113.784 0.000 5.827 4.858
## .Im7 5.753 0.052 110.826 0.000 5.753 4.756
## DECO 0.000 0.000 0.000
## FOOD 0.000 0.000 0.000
## ATMOS 0.000 0.000 0.000
## PRODQUAL 0.000 0.000 0.000
## CHOICE 0.000 0.000 0.000
## PROF 0.000 0.000 0.000
## BRAND 0.000 0.000 0.000
## FRENCH 0.000 0.000 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .Im3 0.213 0.024 8.755 0.000 0.213 0.122
## .Im4 0.109 0.024 4.532 0.000 0.109 0.060
## .Im5 0.747 0.049 15.217 0.000 0.747 0.422
## .Im10 0.114 0.019 5.961 0.000 0.114 0.148
## .Im14 0.070 0.019 3.680 0.000 0.070 0.093
## .Im20 0.638 0.061 10.451 0.000 0.638 0.285
## .Im21 0.725 0.057 12.672 0.000 0.725 0.386
## .Im22 0.541 0.063 8.539 0.000 0.541 0.231
## .Im11 0.814 0.055 14.802 0.000 0.814 0.622
## .Im12 0.310 0.040 7.845 0.000 0.310 0.240
## .Im13 0.390 0.045 8.765 0.000 0.390 0.269
## .Im1 0.070 0.050 1.394 0.163 0.070 0.040
## .Im2 0.317 0.044 7.233 0.000 0.317 0.192
## .Im16 0.599 0.052 11.498 0.000 0.599 0.414
## .Im19 0.338 0.045 7.457 0.000 0.338 0.267
## .Im17 0.095 0.045 2.112 0.035 0.095 0.062
## .Im18 0.521 0.055 9.540 0.000 0.521 0.267
## .Im6 0.487 0.056 8.677 0.000 0.487 0.339
## .Im7 0.128 0.067 1.930 0.054 0.128 0.088
## DECO 1.528 0.107 14.326 0.000 1.000 1.000
## FOOD 0.659 0.049 13.328 0.000 1.000 1.000
## ATMOS 1.599 0.138 11.623 0.000 1.000 1.000
## PRODQUAL 0.494 0.067 7.361 0.000 1.000 1.000
## CHOICE 1.704 0.118 14.388 0.000 1.000 1.000
## PROF 0.849 0.088 9.638 0.000 1.000 1.000
## BRAND 1.451 0.104 13.988 0.000 1.000 1.000
## FRENCH 0.952 0.095 10.058 0.000 1.000 1.000
Chi square: p-value > 0.05
RMSEA RMSEA <= 0.05 Good fit 0.05 < RMSEA <= 0.08 Acceptable fit 0.08 < RMSEA <= 0.10 Bad fit RMSEA > 0.1 Unacceptable fit
CFI CFI < 0.90 definitely reject model 0.90 < CFI < 0.95 high underrejection rates for misspecified models CFI > 0.95 accept model
# semPaths(CFA_fit_img_7f, what = "path", whatLabels = "std", style = "mx",
# rotation = 2, layout = "tree3", mar = c(1, 2, 1, 2),
# nCharNodes = 7,shapeMan = "rectangle", sizeMan = 8, sizeMan2 = 5,
# curvePivot=TRUE, edge.label.cex = 1.2, edge.color = "skyblue4")
semPaths(CFA_fit_img_7f, what = "path", whatLabels = "std", style = "mx",
rotation = 2, layout = "tree3", mar = c(1, 2, 1, 2),
nCharNodes = 7,shapeMan = "rectangle",
sizeMan = 4, sizeMan2 = 3, sizeInt = 2, sizeLat = 6, asize = 1.5,
curvePivot=TRUE, edge.label.cex = .8, edge.color = "skyblue4"
)lambda = inspect(CFA_fit_img_7f, what="std")$lambda
theta = inspect(CFA_fit_img_7f, what="std")$theta
# create lambda matrix with ones instead of std.all
ones <- lambda
ones[ones>0] <- 1
# a matrix with dimensions of lambda matrix but with lambdas replaced by thetas
theta_lb <- theta %*% ones# calculate indicator reliabilities (should be larger than 0.4)
indicrel <- lambda^2/(lambda^2 + theta_lb)
# indicrel
# replace all values satisfying condition with NaN for visibility
indicrel_fail <- indicrel
indicrel_fail[indicrel_fail>.4] <- NaN
indicrel_fail## DECO FOOD ATMOS PRODQU CHOICE PROF BRAND FRENCH
## Im3 NaN NaN NaN NaN NaN NaN NaN NaN
## Im4 NaN NaN NaN NaN NaN NaN NaN NaN
## Im5 NaN NaN NaN NaN NaN NaN NaN NaN
## Im10 NaN NaN NaN NaN NaN NaN NaN NaN
## Im14 NaN NaN NaN NaN NaN NaN NaN NaN
## Im20 NaN NaN NaN NaN NaN NaN NaN NaN
## Im21 NaN NaN NaN NaN NaN NaN NaN NaN
## Im22 NaN NaN NaN NaN NaN NaN NaN NaN
## Im11 NaN NaN NaN 0.378 NaN NaN NaN NaN
## Im12 NaN NaN NaN NaN NaN NaN NaN NaN
## Im13 NaN NaN NaN NaN NaN NaN NaN NaN
## Im1 NaN NaN NaN NaN NaN NaN NaN NaN
## Im2 NaN NaN NaN NaN NaN NaN NaN NaN
## Im16 NaN NaN NaN NaN NaN NaN NaN NaN
## Im19 NaN NaN NaN NaN NaN NaN NaN NaN
## Im17 NaN NaN NaN NaN NaN NaN NaN NaN
## Im18 NaN NaN NaN NaN NaN NaN NaN NaN
## Im6 NaN NaN NaN NaN NaN NaN NaN NaN
## Im7 NaN NaN NaN NaN NaN NaN NaN NaN
# calculate construct reliability (should be above .6)
constrrel <- (t(lambda) %*% ones)^2 / ((t(lambda) %*% ones)^2 + t(theta_lb) %*% ones )
# constrrel
# replace all values satisfying condition with NaN for visibility
constrrel_fail <- constrrel
constrrel_fail[constrrel_fail>.6] <- NaN
constrrel_fail## DECO FOOD ATMOS PRODQUAL CHOICE PROF BRAND FRENCH
## DECO NaN NaN NaN NaN NaN NaN NaN NaN
## FOOD NaN NaN NaN NaN NaN NaN NaN NaN
## ATMOS NaN NaN NaN NaN NaN NaN NaN NaN
## PRODQUAL NaN NaN NaN NaN NaN NaN NaN NaN
## CHOICE NaN NaN NaN NaN NaN NaN NaN NaN
## PROF NaN NaN NaN NaN NaN NaN NaN NaN
## BRAND NaN NaN NaN NaN NaN NaN NaN NaN
## FRENCH NaN NaN NaN NaN NaN NaN NaN NaN
# calculate Average Variance Extracted (should be above .5)
AVE <- (t(lambda) %*% lambda) / (t(lambda) %*% lambda + t(theta_lb) %*% ones )
# avgvar
# replace all values satisfying condition with NaN for visibility
AVE_fail <- AVE
AVE_fail[AVE_fail>.5] <- NaN
AVE_fail## DECO FOOD ATMOS PRODQUAL CHOICE PROF BRAND FRENCH
## DECO NaN NaN NaN NaN NaN NaN NaN NaN
## FOOD NaN NaN NaN NaN NaN NaN NaN NaN
## ATMOS NaN NaN NaN NaN NaN NaN NaN NaN
## PRODQUAL NaN NaN NaN NaN NaN NaN NaN NaN
## CHOICE NaN NaN NaN NaN NaN NaN NaN NaN
## PROF NaN NaN NaN NaN NaN NaN NaN NaN
## BRAND NaN NaN NaN NaN NaN NaN NaN NaN
## FRENCH NaN NaN NaN NaN NaN NaN NaN NaN
# correlations between constructs (factors...) should be lower than .7
psi = inspect(CFA_fit_img_7f, what="std")$psi
psi_fail <- psi
psi_fail[psi_fail<.7] <- NaN
psi_fail## DECO FOOD ATMOS PRODQU CHOICE PROF BRAND FRENCH
## DECO 1
## FOOD NaN 1
## ATMOS NaN NaN 1
## PRODQUAL NaN NaN NaN 1
## CHOICE NaN NaN NaN NaN 1
## PROF NaN NaN NaN NaN NaN 1
## BRAND NaN NaN NaN NaN NaN NaN 1
## FRENCH NaN NaN NaN NaN NaN NaN NaN 1
# AVE should be higher than squared correlations between constructs
# replace diagonal of psi matrix with AVE values
psi2 <- psi - psi * diag(1,nrow(psi),ncol(psi)) + diag(AVE) * diag(1,nrow(AVE),ncol(AVE))
# create matrix with columns filled with AVE
AVE_full <- AVE
AVE_full[is.na(AVE_full)] <- 0 #replace NAs with 0s
AVE_full <- AVE_full^0 %*% AVE_full # multiply a matrix full of ones with AVE_full to get columns filled with AVE
# substract matrices, replace all values satisfying positive condition (AVE > psi) with NaN
AVEpsi_fail <- AVE_full - psi2
# AVE_full - psi2
AVEpsi_fail[AVEpsi_fail >= 0] <- NaN
AVE_full## DECO FOOD ATMOS PRODQUAL CHOICE PROF BRAND
## DECO 0.7983933 0.8796192 0.6990218 0.622977 0.8842421 0.6598497 0.8358722
## FOOD 0.7983933 0.8796192 0.6990218 0.622977 0.8842421 0.6598497 0.8358722
## ATMOS 0.7983933 0.8796192 0.6990218 0.622977 0.8842421 0.6598497 0.8358722
## PRODQUAL 0.7983933 0.8796192 0.6990218 0.622977 0.8842421 0.6598497 0.8358722
## CHOICE 0.7983933 0.8796192 0.6990218 0.622977 0.8842421 0.6598497 0.8358722
## PROF 0.7983933 0.8796192 0.6990218 0.622977 0.8842421 0.6598497 0.8358722
## BRAND 0.7983933 0.8796192 0.6990218 0.622977 0.8842421 0.6598497 0.8358722
## FRENCH 0.7983933 0.8796192 0.6990218 0.622977 0.8842421 0.6598497 0.8358722
## FRENCH
## DECO 0.786707
## FOOD 0.786707
## ATMOS 0.786707
## PRODQUAL 0.786707
## CHOICE 0.786707
## PROF 0.786707
## BRAND 0.786707
## FRENCH 0.786707
psi## DECO FOOD ATMOS PRODQU CHOICE PROF BRAND FRENCH
## DECO 1.000
## FOOD 0.416 1.000
## ATMOS 0.467 0.295 1.000
## PRODQUAL 0.471 0.452 0.418 1.000
## CHOICE 0.441 0.309 0.448 0.478 1.000
## PROF 0.653 0.498 0.478 0.529 0.597 1.000
## BRAND 0.517 0.325 0.516 0.566 0.519 0.601 1.000
## FRENCH 0.334 0.585 0.333 0.306 0.225 0.366 0.322 1.000
AVEpsi_fail## DECO FOOD ATMOS PRODQU CHOICE PROF BRAND FRENCH
## DECO .
## FOOD NaN .
## ATMOS NaN NaN .
## PRODQUAL NaN NaN NaN .
## CHOICE NaN NaN NaN NaN .
## PROF NaN NaN NaN NaN NaN .
## BRAND NaN NaN NaN NaN NaN NaN .
## FRENCH NaN NaN NaN NaN NaN NaN NaN .
arrange(modificationindices(CFA_fit_img_7f),-mi)## lhs op rhs mi epc sepc.lv sepc.all sepc.nox
## 1 BRAND =~ Im13 23.832 0.220 0.265 0.220 0.220
## 2 Im11 ~~ Im13 21.323 -0.191 -0.191 -0.338 -0.338
## 3 BRAND =~ Im12 17.245 -0.179 -0.216 -0.190 -0.190
## 4 Im21 ~~ Im22 15.139 -0.285 -0.285 -0.455 -0.455
## 5 CHOICE =~ Im20 14.777 -0.151 -0.197 -0.132 -0.132
## 6 CHOICE =~ Im13 13.970 0.133 0.174 0.144 0.144
## 7 Im11 ~~ Im12 13.307 0.145 0.145 0.288 0.288
## 8 FOOD =~ Im11 12.742 0.215 0.174 0.152 0.152
## 9 Im20 ~~ Im21 11.455 0.228 0.228 0.335 0.335
## 10 ATMOS =~ Im12 10.952 -0.115 -0.145 -0.127 -0.127
## 11 Im13 ~~ Im1 10.707 0.068 0.068 0.409 0.409
## 12 CHOICE =~ Im12 10.663 -0.111 -0.145 -0.127 -0.127
## 13 Im13 ~~ Im17 9.392 0.068 0.068 0.355 0.355
## 14 Im4 ~~ Im17 9.096 -0.046 -0.046 -0.446 -0.446
## 15 BRAND =~ Im20 8.230 -0.133 -0.160 -0.107 -0.107
## 16 Im10 ~~ Im16 7.956 0.046 0.046 0.175 0.175
## 17 BRAND =~ Im22 7.656 0.131 0.158 0.103 0.103
## 18 FRENCH =~ Im22 7.278 0.136 0.132 0.087 0.087
## 19 ATMOS =~ Im11 6.691 0.101 0.128 0.112 0.112
## 20 Im22 ~~ Im12 6.644 -0.076 -0.076 -0.185 -0.185
## 21 CHOICE =~ Im5 6.302 0.086 0.112 0.084 0.084
## 22 BRAND =~ Im4 6.247 -0.067 -0.081 -0.060 -0.060
## 23 PRODQUAL =~ Im5 6.120 0.171 0.120 0.091 0.091
## 24 Im14 ~~ Im16 6.048 -0.039 -0.039 -0.191 -0.191
## 25 Im10 ~~ Im6 6.011 -0.035 -0.035 -0.147 -0.147
## 26 BRAND =~ Im5 5.755 0.095 0.115 0.086 0.086
## 27 Im3 ~~ Im1 5.614 -0.034 -0.034 -0.281 -0.281
## 28 DECO =~ Im7 5.531 -0.093 -0.114 -0.095 -0.095
## 29 DECO =~ Im6 5.531 0.078 0.097 0.080 0.080
## 30 ATMOS =~ Im5 5.517 0.089 0.113 0.085 0.085
## 31 DECO =~ Im18 5.361 0.099 0.123 0.088 0.088
## 32 DECO =~ Im17 5.361 -0.100 -0.124 -0.099 -0.099
## 33 FRENCH =~ Im20 5.231 -0.113 -0.111 -0.074 -0.074
## 34 Im22 ~~ Im11 5.182 0.087 0.087 0.131 0.131
## 35 FOOD =~ Im13 5.137 -0.127 -0.103 -0.086 -0.086
## 36 Im3 ~~ Im4 5.131 0.162 0.162 1.061 1.061
## 37 DECO =~ Im20 5.124 -0.096 -0.118 -0.079 -0.079
## 38 BRAND =~ Im7 5.064 -0.090 -0.108 -0.089 -0.089
## 39 BRAND =~ Im6 5.064 0.076 0.091 0.076 0.076
## 40 Im22 ~~ Im1 5.051 0.056 0.056 0.290 0.290
## 41 Im13 ~~ Im16 5.040 -0.067 -0.067 -0.138 -0.138
## 42 Im11 ~~ Im6 4.965 -0.069 -0.069 -0.109 -0.109
## 43 Im10 ~~ Im13 4.793 -0.031 -0.031 -0.146 -0.146
## 44 Im4 ~~ Im18 4.776 0.040 0.040 0.166 0.166
## 45 Im5 ~~ Im6 4.758 -0.065 -0.065 -0.108 -0.108
## 46 Im3 ~~ Im22 4.749 0.049 0.049 0.143 0.143
## 47 Im10 ~~ Im7 4.706 0.032 0.032 0.265 0.265
## 48 CHOICE =~ Im22 4.697 0.087 0.113 0.074 0.074
## 49 Im3 ~~ Im5 4.674 -0.071 -0.071 -0.178 -0.178
## 50 Im13 ~~ Im2 4.562 -0.044 -0.044 -0.125 -0.125
## 51 FOOD =~ Im5 4.520 0.117 0.095 0.072 0.072
## 52 Im20 ~~ Im17 4.488 -0.057 -0.057 -0.230 -0.230
## 53 ATMOS =~ Im4 4.309 -0.052 -0.066 -0.049 -0.049
## 54 DECO =~ Im22 4.302 0.090 0.111 0.072 0.072
## 55 PROF =~ Im2 4.223 0.170 0.157 0.122 0.122
## 56 PROF =~ Im1 4.223 -0.192 -0.177 -0.133 -0.133
## 57 Im20 ~~ Im6 4.215 -0.064 -0.064 -0.115 -0.115
## 58 PRODQUAL =~ Im1 4.027 0.145 0.102 0.077 0.077
## 59 PRODQUAL =~ Im2 4.027 -0.129 -0.090 -0.070 -0.070
## 60 PROF =~ Im12 3.965 -0.117 -0.108 -0.095 -0.095
## 61 Im14 ~~ Im6 3.823 0.027 0.027 0.149 0.149
## 62 FOOD =~ Im6 3.804 -0.271 -0.220 -0.183 -0.183
## 63 FOOD =~ Im7 3.804 0.321 0.260 0.215 0.215
## 64 Im2 ~~ Im17 3.691 0.033 0.033 0.192 0.192
## 65 Im4 ~~ Im6 3.588 0.033 0.033 0.143 0.143
## 66 Im3 ~~ Im17 3.342 0.028 0.028 0.198 0.198
## 67 Im11 ~~ Im1 3.335 -0.045 -0.045 -0.189 -0.189
## 68 Im5 ~~ Im1 3.275 0.043 0.043 0.188 0.188
## 69 PROF =~ Im20 3.209 -0.113 -0.104 -0.069 -0.069
## 70 CHOICE =~ Im21 3.202 0.067 0.087 0.064 0.064
## 71 Im3 ~~ Im2 3.151 0.026 0.026 0.100 0.100
## 72 Im20 ~~ Im13 3.089 0.055 0.055 0.111 0.111
## 73 Im18 ~~ Im6 3.067 0.046 0.046 0.091 0.091
## 74 Im14 ~~ Im7 3.014 -0.026 -0.026 -0.272 -0.272
## 75 Im11 ~~ Im17 2.983 -0.045 -0.045 -0.163 -0.163
## 76 FRENCH =~ Im11 2.967 0.080 0.078 0.069 0.069
## 77 ATMOS =~ Im13 2.904 0.062 0.078 0.065 0.065
## 78 Im5 ~~ Im7 2.807 0.048 0.048 0.154 0.154
## 79 Im10 ~~ Im11 2.784 0.028 0.028 0.093 0.093
## 80 Im20 ~~ Im1 2.774 -0.042 -0.042 -0.198 -0.198
## 81 Im5 ~~ Im14 2.721 0.026 0.026 0.115 0.115
## 82 Im1 ~~ Im17 2.656 -0.029 -0.029 -0.359 -0.359
## 83 FRENCH =~ Im19 2.578 0.085 0.083 0.074 0.074
## 84 FRENCH =~ Im16 2.578 -0.082 -0.080 -0.066 -0.066
## 85 Im2 ~~ Im16 2.577 0.038 0.038 0.088 0.088
## 86 CHOICE =~ Im14 2.577 0.027 0.035 0.041 0.041
## 87 CHOICE =~ Im10 2.577 -0.026 -0.035 -0.039 -0.039
## 88 Im21 ~~ Im18 2.573 -0.052 -0.052 -0.084 -0.084
## 89 Im4 ~~ Im11 2.457 -0.034 -0.034 -0.113 -0.113
## 90 PROF =~ Im13 2.455 0.096 0.089 0.074 0.074
## 91 Im22 ~~ Im19 2.419 -0.049 -0.049 -0.115 -0.115
## 92 Im4 ~~ Im22 2.418 -0.034 -0.034 -0.138 -0.138
## 93 Im3 ~~ Im20 2.350 -0.034 -0.034 -0.093 -0.093
## 94 Im12 ~~ Im7 2.333 0.036 0.036 0.178 0.178
## 95 DECO =~ Im12 2.244 -0.054 -0.066 -0.058 -0.058
## 96 Im11 ~~ Im7 2.221 0.044 0.044 0.137 0.137
## 97 Im19 ~~ Im17 2.187 0.035 0.035 0.193 0.193
## 98 PRODQUAL =~ Im16 2.157 -0.133 -0.094 -0.078 -0.078
## 99 PRODQUAL =~ Im19 2.157 0.140 0.098 0.087 0.087
## 100 Im10 ~~ Im17 2.035 -0.017 -0.017 -0.161 -0.161
## 101 Im14 ~~ Im17 1.988 0.016 0.016 0.201 0.201
## 102 Im4 ~~ Im1 1.978 0.020 0.020 0.227 0.227
## 103 Im3 ~~ Im12 1.906 -0.024 -0.024 -0.092 -0.092
## 104 Im12 ~~ Im6 1.902 -0.033 -0.033 -0.084 -0.084
## 105 CHOICE =~ Im16 1.817 0.068 0.089 0.074 0.074
## 106 CHOICE =~ Im19 1.817 -0.071 -0.093 -0.083 -0.083
## 107 Im14 ~~ Im2 1.800 0.015 0.015 0.098 0.098
## 108 Im18 ~~ Im7 1.743 -0.033 -0.033 -0.128 -0.128
## 109 FRENCH =~ Im5 1.735 0.059 0.057 0.043 0.043
## 110 Im11 ~~ Im2 1.713 0.033 0.033 0.064 0.064
## 111 ATMOS =~ Im17 1.684 -0.057 -0.073 -0.058 -0.058
## 112 ATMOS =~ Im18 1.684 0.057 0.072 0.052 0.052
## 113 Im19 ~~ Im18 1.680 -0.034 -0.034 -0.082 -0.082
## 114 BRAND =~ Im3 1.663 0.034 0.041 0.031 0.031
## 115 Im3 ~~ Im14 1.662 -0.012 -0.012 -0.102 -0.102
## 116 FRENCH =~ Im2 1.647 0.039 0.038 0.030 0.030
## 117 FRENCH =~ Im1 1.647 -0.045 -0.043 -0.033 -0.033
## 118 Im22 ~~ Im2 1.646 -0.032 -0.032 -0.077 -0.077
## 119 Im22 ~~ Im18 1.613 0.041 0.041 0.077 0.077
## 120 FOOD =~ Im2 1.604 0.050 0.040 0.031 0.031
## 121 FOOD =~ Im1 1.604 -0.056 -0.046 -0.034 -0.034
## 122 PRODQUAL =~ Im4 1.602 -0.058 -0.041 -0.030 -0.030
## 123 Im22 ~~ Im13 1.588 -0.040 -0.040 -0.086 -0.086
## 124 Im4 ~~ Im2 1.557 -0.018 -0.018 -0.095 -0.095
## 125 Im14 ~~ Im21 1.552 0.021 0.021 0.091 0.091
## 126 Im5 ~~ Im16 1.529 -0.043 -0.043 -0.064 -0.064
## 127 Im12 ~~ Im17 1.526 -0.026 -0.026 -0.151 -0.151
## 128 Im10 ~~ Im18 1.519 0.018 0.018 0.072 0.072
## 129 PRODQUAL =~ Im22 1.519 -0.095 -0.067 -0.044 -0.044
## 130 Im2 ~~ Im18 1.481 -0.026 -0.026 -0.063 -0.063
## 131 Im12 ~~ Im13 1.475 0.089 0.089 0.257 0.257
## 132 PRODQUAL =~ Im6 1.473 -0.073 -0.052 -0.043 -0.043
## 133 PRODQUAL =~ Im7 1.473 0.087 0.061 0.051 0.051
## 134 Im14 ~~ Im18 1.464 -0.017 -0.017 -0.088 -0.088
## 135 PROF =~ Im22 1.445 0.077 0.071 0.047 0.047
## 136 DECO =~ Im13 1.431 0.045 0.055 0.046 0.046
## 137 PRODQUAL =~ Im17 1.422 0.109 0.076 0.062 0.062
## 138 PRODQUAL =~ Im18 1.422 -0.108 -0.076 -0.054 -0.054
## 139 Im4 ~~ Im12 1.373 0.019 0.019 0.106 0.106
## 140 ATMOS =~ Im1 1.355 0.043 0.054 0.040 0.040
## 141 ATMOS =~ Im2 1.355 -0.038 -0.048 -0.037 -0.037
## 142 Im22 ~~ Im7 1.342 0.035 0.035 0.133 0.133
## 143 Im3 ~~ Im18 1.316 -0.022 -0.022 -0.065 -0.065
## 144 Im3 ~~ Im11 1.290 0.025 0.025 0.061 0.061
## 145 PROF =~ Im4 1.267 -0.055 -0.050 -0.037 -0.037
## 146 Im13 ~~ Im19 1.244 0.029 0.029 0.080 0.080
## 147 Im3 ~~ Im10 1.231 0.011 0.011 0.071 0.071
## 148 Im10 ~~ Im12 1.205 0.014 0.014 0.077 0.077
## 149 Im12 ~~ Im16 1.199 0.030 0.030 0.071 0.071
## 150 BRAND =~ Im11 1.070 -0.047 -0.056 -0.049 -0.049
## 151 BRAND =~ Im2 1.067 0.042 0.051 0.039 0.039
## 152 BRAND =~ Im1 1.067 -0.048 -0.057 -0.043 -0.043
## 153 Im14 ~~ Im12 1.061 -0.013 -0.013 -0.090 -0.090
## 154 Im4 ~~ Im7 1.054 -0.017 -0.017 -0.147 -0.147
## 155 PRODQUAL =~ Im20 1.037 0.077 0.054 0.036 0.036
## 156 Im21 ~~ Im17 1.017 0.027 0.027 0.101 0.101
## 157 Im20 ~~ Im19 0.988 0.031 0.031 0.068 0.068
## 158 PROF =~ Im17 0.986 0.084 0.077 0.062 0.062
## 159 PROF =~ Im18 0.986 -0.083 -0.077 -0.055 -0.055
## 160 Im19 ~~ Im7 0.949 0.025 0.025 0.122 0.122
## 161 PROF =~ Im7 0.940 -0.060 -0.055 -0.045 -0.045
## 162 PROF =~ Im6 0.940 0.050 0.046 0.039 0.039
## 163 Im13 ~~ Im18 0.925 -0.026 -0.026 -0.057 -0.057
## 164 Im5 ~~ Im2 0.918 -0.023 -0.023 -0.047 -0.047
## 165 Im14 ~~ Im13 0.889 0.013 0.013 0.079 0.079
## 166 Im16 ~~ Im7 0.880 -0.027 -0.027 -0.097 -0.097
## 167 Im1 ~~ Im18 0.847 0.019 0.019 0.101 0.101
## 168 ATMOS =~ Im3 0.826 0.022 0.028 0.022 0.022
## 169 FOOD =~ Im20 0.814 -0.052 -0.042 -0.028 -0.028
## 170 Im22 ~~ Im6 0.806 0.028 0.028 0.054 0.054
## 171 Im5 ~~ Im19 0.786 -0.026 -0.026 -0.052 -0.052
## 172 BRAND =~ Im16 0.775 -0.050 -0.060 -0.050 -0.050
## 173 BRAND =~ Im19 0.775 0.052 0.063 0.056 0.056
## 174 Im3 ~~ Im19 0.774 0.016 0.016 0.061 0.061
## 175 BRAND =~ Im14 0.773 0.017 0.020 0.023 0.023
## 176 BRAND =~ Im10 0.773 -0.016 -0.020 -0.022 -0.022
## 177 Im10 ~~ Im19 0.726 -0.012 -0.012 -0.062 -0.062
## 178 FRENCH =~ Im13 0.706 -0.035 -0.034 -0.028 -0.028
## 179 PROF =~ Im5 0.688 0.055 0.051 0.038 0.038
## 180 Im4 ~~ Im5 0.687 0.029 0.029 0.103 0.103
## 181 Im20 ~~ Im12 0.675 0.024 0.024 0.054 0.054
## 182 Im2 ~~ Im7 0.669 0.016 0.016 0.079 0.079
## 183 Im3 ~~ Im7 0.637 -0.014 -0.014 -0.084 -0.084
## 184 PRODQUAL =~ Im14 0.619 0.031 0.022 0.025 0.025
## 185 PRODQUAL =~ Im10 0.619 -0.030 -0.021 -0.024 -0.024
## 186 Im21 ~~ Im7 0.611 -0.023 -0.023 -0.076 -0.076
## 187 Im5 ~~ Im22 0.596 0.028 0.028 0.044 0.044
## 188 Im4 ~~ Im10 0.595 -0.007 -0.007 -0.066 -0.066
## 189 Im20 ~~ Im18 0.582 0.025 0.025 0.043 0.043
## 190 Im10 ~~ Im2 0.581 -0.008 -0.008 -0.045 -0.045
## 191 Im4 ~~ Im16 0.579 0.016 0.016 0.062 0.062
## 192 Im21 ~~ Im2 0.574 0.019 0.019 0.039 0.039
## 193 Im10 ~~ Im21 0.544 -0.013 -0.013 -0.043 -0.043
## 194 Im14 ~~ Im22 0.525 -0.012 -0.012 -0.062 -0.062
## 195 Im13 ~~ Im7 0.518 -0.018 -0.018 -0.080 -0.080
## 196 Im5 ~~ Im11 0.501 0.026 0.026 0.033 0.033
## 197 Im20 ~~ Im11 0.498 0.027 0.027 0.038 0.038
## 198 Im12 ~~ Im2 0.492 -0.013 -0.013 -0.043 -0.043
## 199 Im11 ~~ Im18 0.492 0.023 0.023 0.035 0.035
## 200 CHOICE =~ Im3 0.483 -0.015 -0.020 -0.015 -0.015
## 201 Im1 ~~ Im16 0.483 -0.017 -0.017 -0.082 -0.082
## 202 Im21 ~~ Im12 0.479 0.020 0.020 0.043 0.043
## 203 Im5 ~~ Im10 0.474 -0.011 -0.011 -0.039 -0.039
## 204 CHOICE =~ Im11 0.473 -0.026 -0.034 -0.030 -0.030
## 205 Im10 ~~ Im20 0.466 0.012 0.012 0.043 0.043
## 206 PROF =~ Im3 0.453 0.032 0.029 0.022 0.022
## 207 FRENCH =~ Im3 0.431 -0.019 -0.018 -0.014 -0.014
## 208 FOOD =~ Im3 0.430 -0.023 -0.019 -0.014 -0.014
## 209 FOOD =~ Im19 0.429 0.047 0.038 0.034 0.034
## 210 FOOD =~ Im16 0.429 -0.045 -0.037 -0.031 -0.031
## 211 PROF =~ Im11 0.410 0.039 0.036 0.032 0.032
## 212 Im5 ~~ Im20 0.382 0.023 0.023 0.033 0.033
## 213 Im13 ~~ Im6 0.377 0.016 0.016 0.036 0.036
## 214 Im14 ~~ Im19 0.372 0.009 0.009 0.056 0.056
## 215 Im21 ~~ Im13 0.372 -0.019 -0.019 -0.036 -0.036
## 216 PROF =~ Im21 0.371 0.036 0.033 0.024 0.024
## 217 CHOICE =~ Im4 0.369 -0.014 -0.018 -0.013 -0.013
## 218 Im22 ~~ Im17 0.360 0.016 0.016 0.071 0.071
## 219 FRENCH =~ Im21 0.360 -0.029 -0.028 -0.020 -0.020
## 220 Im21 ~~ Im11 0.346 -0.022 -0.022 -0.029 -0.029
## 221 Im5 ~~ Im17 0.345 0.015 0.015 0.055 0.055
## 222 Im14 ~~ Im20 0.330 -0.010 -0.010 -0.045 -0.045
## 223 FOOD =~ Im21 0.320 0.032 0.026 0.019 0.019
## 224 CHOICE =~ Im17 0.309 0.023 0.030 0.024 0.024
## 225 CHOICE =~ Im18 0.309 -0.023 -0.030 -0.021 -0.021
## 226 Im3 ~~ Im13 0.299 0.010 0.010 0.035 0.035
## 227 Im4 ~~ Im19 0.281 -0.010 -0.010 -0.050 -0.050
## 228 Im22 ~~ Im16 0.277 0.019 0.019 0.033 0.033
## 229 Im5 ~~ Im21 0.277 -0.019 -0.019 -0.026 -0.026
## 230 Im4 ~~ Im14 0.246 0.005 0.005 0.053 0.053
## 231 DECO =~ Im11 0.238 0.019 0.024 0.021 0.021
## 232 Im16 ~~ Im18 0.231 -0.015 -0.015 -0.026 -0.026
## 233 Im17 ~~ Im7 0.228 -0.010 -0.010 -0.094 -0.094
## 234 Im21 ~~ Im16 0.227 -0.017 -0.017 -0.026 -0.026
## 235 Im20 ~~ Im22 0.211 0.043 0.043 0.074 0.074
## 236 Im17 ~~ Im6 0.208 0.010 0.010 0.045 0.045
## 237 Im20 ~~ Im2 0.203 -0.011 -0.011 -0.025 -0.025
## 238 Im2 ~~ Im19 0.202 -0.009 -0.009 -0.029 -0.029
## 239 FOOD =~ Im4 0.194 -0.016 -0.013 -0.010 -0.010
## 240 Im4 ~~ Im13 0.168 -0.007 -0.007 -0.035 -0.035
## 241 Im14 ~~ Im11 0.165 0.007 0.007 0.028 0.028
## 242 FOOD =~ Im22 0.151 0.023 0.018 0.012 0.012
## 243 Im12 ~~ Im18 0.146 -0.010 -0.010 -0.024 -0.024
## 244 Im20 ~~ Im16 0.145 0.014 0.014 0.022 0.022
## 245 Im21 ~~ Im1 0.132 0.009 0.009 0.040 0.040
## 246 ATMOS =~ Im19 0.131 -0.017 -0.022 -0.019 -0.019
## 247 ATMOS =~ Im16 0.131 0.016 0.021 0.017 0.017
## 248 Im4 ~~ Im20 0.129 0.008 0.008 0.029 0.029
## 249 Im1 ~~ Im7 0.126 -0.007 -0.007 -0.075 -0.075
## 250 Im12 ~~ Im1 0.110 -0.006 -0.006 -0.044 -0.044
## 251 Im3 ~~ Im6 0.106 0.006 0.006 0.018 0.018
## 252 Im2 ~~ Im6 0.094 -0.006 -0.006 -0.016 -0.016
## 253 FRENCH =~ Im18 0.094 0.013 0.012 0.009 0.009
## 254 FRENCH =~ Im17 0.094 -0.013 -0.013 -0.010 -0.010
## 255 Im10 ~~ Im1 0.093 -0.003 -0.003 -0.038 -0.038
## 256 PRODQUAL =~ Im21 0.088 0.021 0.015 0.011 0.011
## 257 Im5 ~~ Im18 0.083 0.009 0.009 0.014 0.014
## 258 Im20 ~~ Im7 0.082 0.009 0.009 0.030 0.030
## 259 DECO =~ Im2 0.075 0.009 0.011 0.008 0.008
## 260 DECO =~ Im1 0.075 -0.010 -0.012 -0.009 -0.009
## 261 Im5 ~~ Im12 0.067 0.007 0.007 0.015 0.015
## 262 Im14 ~~ Im1 0.063 -0.003 -0.003 -0.039 -0.039
## 263 ATMOS =~ Im14 0.061 0.004 0.006 0.006 0.006
## 264 ATMOS =~ Im10 0.061 -0.004 -0.006 -0.006 -0.006
## 265 Im21 ~~ Im19 0.060 0.008 0.008 0.015 0.015
## 266 Im4 ~~ Im21 0.059 0.005 0.005 0.018 0.018
## 267 PROF =~ Im10 0.058 0.008 0.007 0.008 0.008
## 268 PROF =~ Im14 0.058 -0.008 -0.007 -0.009 -0.009
## 269 Im1 ~~ Im19 0.056 -0.005 -0.005 -0.034 -0.034
## 270 CHOICE =~ Im6 0.055 -0.007 -0.009 -0.007 -0.007
## 271 CHOICE =~ Im7 0.055 0.008 0.010 0.008 0.008
## 272 DECO =~ Im14 0.052 0.005 0.006 0.007 0.007
## 273 DECO =~ Im10 0.052 -0.005 -0.006 -0.006 -0.006
## 274 Im10 ~~ Im22 0.051 0.004 0.004 0.015 0.015
## 275 FRENCH =~ Im12 0.045 -0.008 -0.008 -0.007 -0.007
## 276 Im1 ~~ Im6 0.039 -0.004 -0.004 -0.021 -0.021
## 277 ATMOS =~ Im6 0.036 -0.006 -0.008 -0.007 -0.007
## 278 ATMOS =~ Im7 0.036 0.008 0.010 0.008 0.008
## 279 Im12 ~~ Im19 0.023 -0.004 -0.004 -0.011 -0.011
## 280 DECO =~ Im21 0.016 0.005 0.006 0.005 0.005
## 281 FOOD =~ Im17 0.015 0.006 0.005 0.004 0.004
## 282 FOOD =~ Im18 0.015 -0.006 -0.005 -0.004 -0.004
## 283 Im3 ~~ Im21 0.013 -0.003 -0.003 -0.006 -0.006
## 284 Im16 ~~ Im6 0.011 -0.003 -0.003 -0.006 -0.006
## 285 Im19 ~~ Im6 0.009 -0.002 -0.002 -0.006 -0.006
## 286 Im11 ~~ Im19 0.006 -0.002 -0.002 -0.005 -0.005
## 287 Im21 ~~ Im6 0.006 0.002 0.002 0.004 0.004
## 288 DECO =~ Im16 0.004 0.004 0.005 0.004 0.004
## 289 DECO =~ Im19 0.004 -0.004 -0.005 -0.004 -0.004
## 290 Im11 ~~ Im16 0.002 0.002 0.002 0.002 0.002
## 291 FRENCH =~ Im14 0.001 0.001 0.001 0.002 0.002
## 292 FRENCH =~ Im10 0.001 -0.001 -0.001 -0.002 -0.002
## 293 Im3 ~~ Im16 0.001 -0.001 -0.001 -0.002 -0.002
## 294 FRENCH =~ Im4 0.001 -0.001 -0.001 0.000 0.000
## 295 Im16 ~~ Im17 0.000 0.000 0.000 0.002 0.002
## 296 PRODQUAL =~ Im3 0.000 0.000 0.000 0.000 0.000
## 297 Im5 ~~ Im13 0.000 0.000 0.000 0.000 0.000
## 298 BRAND =~ Im21 0.000 0.000 0.000 0.000 0.000
## 299 FOOD =~ Im12 0.000 0.000 0.000 0.000 0.000
## don't actually think we need this as we can use the full data for confirmatory and path analysis
# data_img_EFA2
# data.frame(EFA_PAFn[[3]]$scores)
#
# numcol_data_img_EFA = dim(data_img_EFA2)[2]
# numcol_scores = dim(EFA_PAFn[[3]]$scores)[2]
# numcol_data_img_EFA
# numcol_scores
#
# CFA_data = cbind(data_img_EFA2, EFA_PAFn[[3]]$scores, survey_excl_img2["SAT_1"])
# CFA_data
# # colnames(CFA_data)[23:29] = c("Gourmet food", "Brand image", "Choice range", "Relaxed atmosphere", "Decoration", "Product quality", "Frenchness")
#
# # colnames(CFA_data)[numcol_data_img_EFA:(numcol_data_img_EFA + numcol_scores)] = c("FOOD", "BRAND", "CHOICE", "ATMOS", "DECO")
# colnames(CFA_data)[numcol_data_img_EFA:(numcol_data_img_EFA + numcol_scores)] = c("FOOD", "BRAND", "CHOICE", "ATMOS", "DECO", "QUAL", "FRENCH")
#
# CFA_data# missing Im8, Im15, Im9
model_SEM <- "
DECO =~ Im3 + Im4 + Im5
FOOD =~ Im10 + Im14
ATMOS =~ Im20 + Im21 + Im22
PRODQUAL =~ Im11 + Im12 + Im13
CHOICE =~ Im1 + Im2
PROF =~ Im16 + Im19
BRAND =~ Im17 + Im18
FRENCH =~ Im6 + Im7
AFCOM =~ COM_A1 + COM_A2 + COM_A3 + COM_A4
SAT =~ SAT_1 + SAT_2 + SAT_3
RI =~ C_REP1 + C_REP2 + C_REP3
COI =~ C_CR1 + C_CR3 + C_CR4
SAT ~ DECO + FOOD + ATMOS + PRODQUAL + CHOICE + PROF + BRAND + FRENCH + Im8 + Im15 + Im9
AFCOM ~ DECO + FOOD + ATMOS + PRODQUAL + CHOICE + PROF + BRAND + FRENCH + Im8 + Im15 + Im9
"# # linear regression
# lm_SAT_1 <- lm (model_SAT_1, data = survey)
# summary(lm_SAT_1)
# # note: lm deletes all missing variables in the Xs! (not in Ys) (see help lavOptions)# path analysis
SEM_fit <- cfa(model_SEM, data=survey, missing="ML")
summary(SEM_fit, fit.measures=TRUE, standardized=TRUE)## lavaan 0.6.15 ended normally after 170 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 164
##
## Used Total
## Number of observations 523 553
## Number of missing patterns 116
##
## Model Test User Model:
##
## Test statistic 1947.166
## Degrees of freedom 492
## P-value (Chi-square) 0.000
##
## Model Test Baseline Model:
##
## Test statistic 12715.671
## Degrees of freedom 592
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.880
## Tucker-Lewis Index (TLI) 0.856
##
## Robust Comparative Fit Index (CFI) 0.882
## Robust Tucker-Lewis Index (TLI) 0.858
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -21247.689
## Loglikelihood unrestricted model (H1) -20274.106
##
## Akaike (AIC) 42823.378
## Bayesian (BIC) 43521.950
## Sample-size adjusted Bayesian (SABIC) 43001.375
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.075
## 90 Percent confidence interval - lower 0.072
## 90 Percent confidence interval - upper 0.079
## P-value H_0: RMSEA <= 0.050 0.000
## P-value H_0: RMSEA >= 0.080 0.012
##
## Robust RMSEA 0.076
## 90 Percent confidence interval - lower 0.072
## 90 Percent confidence interval - upper 0.079
## P-value H_0: Robust RMSEA <= 0.050 0.000
## P-value H_0: Robust RMSEA >= 0.080 0.027
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.141
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Observed
## Observed information based on Hessian
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## DECO =~
## Im3 1.000 1.247 0.942
## Im4 1.049 0.025 42.442 0.000 1.309 0.967
## Im5 0.802 0.034 23.246 0.000 1.000 0.757
## FOOD =~
## Im10 1.000 0.821 0.925
## Im14 1.005 0.035 28.441 0.000 0.825 0.955
## ATMOS =~
## Im20 1.000 1.255 0.844
## Im21 0.857 0.042 20.471 0.000 1.075 0.786
## Im22 1.074 0.046 23.292 0.000 1.347 0.881
## PRODQUAL =~
## Im11 1.000 0.713 0.619
## Im12 1.383 0.093 14.904 0.000 0.986 0.872
## Im13 1.451 0.104 13.906 0.000 1.035 0.859
## CHOICE =~
## Im1 1.000 1.298 0.977
## Im2 0.884 0.033 26.613 0.000 1.148 0.898
## PROF =~
## Im16 1.000 0.929 0.769
## Im19 1.035 0.058 17.731 0.000 0.962 0.849
## BRAND =~
## Im17 1.000 1.204 0.968
## Im18 0.997 0.042 23.544 0.000 1.200 0.857
## FRENCH =~
## Im6 1.000 0.975 0.810
## Im7 1.192 0.073 16.341 0.000 1.162 0.961
## AFCOM =~
## COM_A1 1.000 1.106 0.783
## COM_A2 1.173 0.056 20.777 0.000 1.298 0.825
## COM_A3 1.169 0.060 19.433 0.000 1.293 0.814
## COM_A4 1.306 0.065 20.206 0.000 1.445 0.844
## SAT =~
## SAT_1 1.000 0.845 0.853
## SAT_2 0.946 0.050 18.893 0.000 0.799 0.811
## SAT_3 0.843 0.055 15.435 0.000 0.712 0.643
## RI =~
## C_REP1 1.000 0.584 0.791
## C_REP2 1.031 0.049 21.106 0.000 0.602 0.957
## C_REP3 0.735 0.039 18.713 0.000 0.429 0.765
## COI =~
## C_CR1 1.000 1.659 0.847
## C_CR3 1.029 0.052 19.607 0.000 1.707 0.825
## C_CR4 0.962 0.050 19.112 0.000 1.596 0.804
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## SAT ~
## DECO -0.106 0.044 -2.397 0.017 -0.156 -0.156
## FOOD 0.072 0.073 0.985 0.324 0.070 0.070
## ATMOS 0.028 0.039 0.698 0.485 0.041 0.041
## PRODQUAL -0.028 0.078 -0.355 0.723 -0.023 -0.023
## CHOICE 0.110 0.042 2.595 0.009 0.169 0.169
## PROF 0.437 0.094 4.634 0.000 0.480 0.480
## BRAND 0.014 0.046 0.308 0.758 0.020 0.020
## FRENCH 0.074 0.058 1.281 0.200 0.086 0.086
## Im8 0.030 0.054 0.555 0.579 0.036 0.037
## Im15 0.052 0.046 1.152 0.249 0.062 0.074
## Im9 0.003 0.033 0.086 0.931 0.003 0.005
## AFCOM ~
## DECO -0.005 0.056 -0.081 0.935 -0.005 -0.005
## FOOD 0.027 0.095 0.283 0.778 0.020 0.020
## ATMOS 0.398 0.054 7.329 0.000 0.451 0.451
## PRODQUAL -0.177 0.103 -1.719 0.086 -0.114 -0.114
## CHOICE 0.087 0.054 1.598 0.110 0.102 0.102
## PROF 0.048 0.115 0.415 0.678 0.040 0.040
## BRAND -0.016 0.060 -0.263 0.792 -0.017 -0.017
## FRENCH 0.155 0.076 2.040 0.041 0.137 0.137
## Im8 0.065 0.071 0.912 0.362 0.059 0.061
## Im15 0.033 0.059 0.556 0.578 0.030 0.035
## Im9 0.021 0.043 0.479 0.632 0.019 0.026
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## DECO ~~
## FOOD 0.424 0.052 8.160 0.000 0.414 0.414
## ATMOS 0.737 0.084 8.771 0.000 0.471 0.471
## PRODQUAL 0.419 0.053 7.878 0.000 0.471 0.471
## CHOICE 0.731 0.081 8.988 0.000 0.452 0.452
## PROF 0.770 0.074 10.454 0.000 0.664 0.664
## BRAND 0.785 0.079 9.991 0.000 0.523 0.523
## FRENCH 0.409 0.066 6.223 0.000 0.336 0.336
## RI 0.189 0.036 5.257 0.000 0.260 0.260
## COI 0.084 0.100 0.839 0.402 0.041 0.041
## FOOD ~~
## ATMOS 0.308 0.052 5.894 0.000 0.299 0.299
## PRODQUAL 0.262 0.035 7.443 0.000 0.448 0.448
## CHOICE 0.310 0.051 6.055 0.000 0.291 0.291
## PROF 0.387 0.045 8.532 0.000 0.507 0.507
## BRAND 0.321 0.048 6.639 0.000 0.325 0.325
## FRENCH 0.469 0.049 9.620 0.000 0.586 0.586
## RI 0.126 0.024 5.241 0.000 0.263 0.263
## COI -0.033 0.066 -0.491 0.623 -0.024 -0.024
## ATMOS ~~
## PRODQUAL 0.391 0.055 7.134 0.000 0.437 0.437
## CHOICE 0.753 0.086 8.735 0.000 0.462 0.462
## PROF 0.558 0.070 7.987 0.000 0.479 0.479
## BRAND 0.795 0.083 9.628 0.000 0.526 0.526
## FRENCH 0.408 0.066 6.203 0.000 0.333 0.333
## RI 0.279 0.041 6.840 0.000 0.380 0.380
## COI 0.434 0.107 4.044 0.000 0.209 0.209
## PRODQUAL ~~
## CHOICE 0.444 0.055 8.016 0.000 0.480 0.480
## PROF 0.359 0.045 7.916 0.000 0.542 0.542
## BRAND 0.482 0.055 8.830 0.000 0.561 0.561
## FRENCH 0.217 0.039 5.605 0.000 0.313 0.313
## RI 0.121 0.023 5.337 0.000 0.291 0.291
## COI 0.075 0.061 1.237 0.216 0.063 0.063
## CHOICE ~~
## PROF 0.732 0.074 9.879 0.000 0.607 0.607
## BRAND 0.805 0.080 10.024 0.000 0.516 0.516
## FRENCH 0.271 0.061 4.431 0.000 0.214 0.214
## RI 0.213 0.038 5.679 0.000 0.281 0.281
## COI 0.063 0.104 0.602 0.547 0.029 0.029
## PROF ~~
## BRAND 0.674 0.068 9.894 0.000 0.603 0.603
## FRENCH 0.334 0.053 6.316 0.000 0.368 0.368
## RI 0.197 0.031 6.354 0.000 0.364 0.364
## COI -0.076 0.082 -0.929 0.353 -0.050 -0.050
## BRAND ~~
## FRENCH 0.373 0.063 5.918 0.000 0.318 0.318
## RI 0.196 0.035 5.619 0.000 0.279 0.279
## COI 0.125 0.097 1.291 0.197 0.063 0.063
## FRENCH ~~
## RI 0.124 0.030 4.182 0.000 0.218 0.218
## COI 0.005 0.080 0.064 0.949 0.003 0.003
## RI ~~
## COI 0.072 0.048 1.498 0.134 0.074 0.074
## .AFCOM ~~
## .SAT 0.205 0.038 5.394 0.000 0.330 0.330
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .Im3 4.983 0.058 85.741 0.000 4.983 3.762
## .Im4 4.995 0.059 84.296 0.000 4.995 3.692
## .Im5 5.049 0.058 86.540 0.000 5.049 3.823
## .Im10 6.093 0.039 156.809 0.000 6.093 6.865
## .Im14 6.139 0.038 161.840 0.000 6.139 7.109
## .Im20 4.704 0.065 72.277 0.000 4.704 3.166
## .Im21 5.163 0.060 86.171 0.000 5.163 3.775
## .Im22 4.306 0.067 63.992 0.000 4.306 2.814
## .Im11 5.652 0.051 111.591 0.000 5.652 4.907
## .Im12 5.666 0.050 113.809 0.000 5.666 5.010
## .Im13 5.450 0.053 103.068 0.000 5.450 4.525
## .Im1 4.808 0.058 82.567 0.000 4.808 3.618
## .Im2 4.877 0.056 86.958 0.000 4.877 3.814
## .Im16 5.150 0.053 96.425 0.000 5.150 4.260
## .Im19 5.159 0.050 103.705 0.000 5.159 4.551
## .Im17 5.044 0.054 92.558 0.000 5.044 4.056
## .Im18 4.603 0.062 74.674 0.000 4.603 3.289
## .Im6 5.821 0.053 110.235 0.000 5.821 4.835
## .Im7 5.760 0.053 108.097 0.000 5.760 4.761
## .COM_A1 3.639 0.533 6.822 0.000 3.639 2.576
## .COM_A2 3.129 0.626 5.002 0.000 3.129 1.990
## .COM_A3 2.780 0.623 4.462 0.000 2.780 1.751
## .COM_A4 2.618 0.695 3.769 0.000 2.618 1.529
## .SAT_1 4.881 0.409 11.942 0.000 4.881 4.929
## .SAT_2 5.045 0.385 13.090 0.000 5.045 5.118
## .SAT_3 5.084 0.346 14.690 0.000 5.084 4.594
## .C_REP1 4.277 0.032 132.216 0.000 4.277 5.791
## .C_REP2 4.506 0.028 163.174 0.000 4.506 7.162
## .C_REP3 4.670 0.025 188.722 0.000 4.670 8.319
## .C_CR1 2.698 0.086 31.244 0.000 2.698 1.377
## .C_CR3 3.290 0.091 36.264 0.000 3.290 1.589
## .C_CR4 2.809 0.087 32.216 0.000 2.809 1.415
## DECO 0.000 0.000 0.000
## FOOD 0.000 0.000 0.000
## ATMOS 0.000 0.000 0.000
## PRODQUAL 0.000 0.000 0.000
## CHOICE 0.000 0.000 0.000
## PROF 0.000 0.000 0.000
## BRAND 0.000 0.000 0.000
## FRENCH 0.000 0.000 0.000
## .AFCOM 0.000 0.000 0.000
## .SAT 0.000 0.000 0.000
## RI 0.000 0.000 0.000
## COI 0.000 0.000 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .Im3 0.199 0.025 8.074 0.000 0.199 0.113
## .Im4 0.118 0.025 4.775 0.000 0.118 0.064
## .Im5 0.744 0.050 14.900 0.000 0.744 0.427
## .Im10 0.113 0.020 5.810 0.000 0.113 0.144
## .Im14 0.065 0.019 3.472 0.001 0.065 0.088
## .Im20 0.634 0.058 10.869 0.000 0.634 0.287
## .Im21 0.715 0.057 12.589 0.000 0.715 0.382
## .Im22 0.526 0.060 8.759 0.000 0.526 0.225
## .Im11 0.818 0.057 14.439 0.000 0.818 0.617
## .Im12 0.307 0.039 7.804 0.000 0.307 0.240
## .Im13 0.380 0.045 8.460 0.000 0.380 0.262
## .Im1 0.080 0.050 1.602 0.109 0.080 0.045
## .Im2 0.317 0.044 7.258 0.000 0.317 0.194
## .Im16 0.598 0.051 11.620 0.000 0.598 0.409
## .Im19 0.360 0.045 8.018 0.000 0.360 0.280
## .Im17 0.098 0.046 2.118 0.034 0.098 0.064
## .Im18 0.519 0.056 9.230 0.000 0.519 0.265
## .Im6 0.498 0.058 8.601 0.000 0.498 0.344
## .Im7 0.113 0.069 1.633 0.103 0.113 0.077
## .COM_A1 0.772 0.061 12.623 0.000 0.772 0.387
## .COM_A2 0.790 0.068 11.538 0.000 0.790 0.319
## .COM_A3 0.849 0.071 11.957 0.000 0.849 0.337
## .COM_A4 0.844 0.077 10.980 0.000 0.844 0.288
## .SAT_1 0.267 0.034 7.954 0.000 0.267 0.272
## .SAT_2 0.333 0.034 9.833 0.000 0.333 0.343
## .SAT_3 0.718 0.053 13.633 0.000 0.718 0.586
## .C_REP1 0.205 0.017 12.097 0.000 0.205 0.375
## .C_REP2 0.033 0.011 3.004 0.003 0.033 0.085
## .C_REP3 0.131 0.010 13.529 0.000 0.131 0.415
## .C_CR1 1.085 0.120 9.059 0.000 1.085 0.283
## .C_CR3 1.371 0.136 10.115 0.000 1.371 0.320
## .C_CR4 1.395 0.128 10.868 0.000 1.395 0.354
## DECO 1.556 0.110 14.096 0.000 1.000 1.000
## FOOD 0.674 0.052 13.069 0.000 1.000 1.000
## ATMOS 1.574 0.138 11.430 0.000 1.000 1.000
## PRODQUAL 0.508 0.070 7.276 0.000 1.000 1.000
## CHOICE 1.685 0.120 14.027 0.000 1.000 1.000
## PROF 0.863 0.090 9.575 0.000 1.000 1.000
## BRAND 1.448 0.106 13.635 0.000 1.000 1.000
## FRENCH 0.951 0.098 9.751 0.000 1.000 1.000
## .AFCOM 0.859 0.089 9.681 0.000 0.702 0.702
## .SAT 0.449 0.048 9.330 0.000 0.629 0.629
## RI 0.341 0.033 10.256 0.000 1.000 1.000
## COI 2.752 0.250 11.005 0.000 1.000 1.000
# note: cfa deletes all missing variables in the Xs! (not in Ys) (see help lavOptions)Chi square: p-value > 0.05
RMSEA RMSEA <= 0.05 Good fit 0.05 < RMSEA <= 0.08 Acceptable fit 0.08 < RMSEA <= 0.10 Bad fit RMSEA > 0.1 Unacceptable fit
CFI CFI < 0.90 definitely reject model 0.90 < CFI < 0.95 high underrejection rates for misspecified models CFI > 0.95 accept model
# semPaths(SEM_fit, what = "path", whatLabels = "std", style = "mx",
# rotation = 2, layout = "tree3", mar = c(1, 2, 1, 2),
# nCharNodes = 7,shapeMan = "rectangle", sizeMan = 8, sizeMan2 = 5,
# curvePivot=TRUE, edge.label.cex = 1.2, edge.color = "skyblue4")
semPaths(SEM_fit, what = "path", whatLabels = "std", style = "mx",
rotation = 2, layout = "tree3", mar = c(1, 2, 1, 2),
nCharNodes = 7,shapeMan = "rectangle",
sizeMan = 4, sizeMan2 = 3, sizeInt = 2, sizeLat = 6, asize = 1.5,
curvePivot=TRUE, edge.label.cex = .8, edge.color = "skyblue4"
)lambda = inspect(SEM_fit, what="std")$lambda
theta = inspect(SEM_fit, what="std")$theta
# create lambda matrix with ones instead of std.all
ones <- lambda
ones[ones>0] <- 1
# a matrix with dimensions of lambda matrix but with lambdas replaced by thetas
theta_lb <- theta %*% ones# calculate indicator reliabilities (should be larger than 0.4)
indicrel <- lambda^2/(lambda^2 + theta_lb)
# indicrel
# replace all values satisfying condition with NaN for visibility
indicrel_fail <- indicrel
indicrel_fail[indicrel_fail>.4] <- NaN
indicrel_fail## DECO FOOD ATMOS PRODQU CHOICE PROF BRAND FRENCH AFCOM SAT RI COI Im8
## Im3 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## Im4 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## Im5 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## Im10 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## Im14 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## Im20 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## Im21 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## Im22 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## Im11 NaN NaN NaN 0.383 NaN NaN NaN NaN NaN NaN NaN NaN NaN
## Im12 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## Im13 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## Im1 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## Im2 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## Im16 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## Im19 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## Im17 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## Im18 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## Im6 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## Im7 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## COM_A1 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## COM_A2 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## COM_A3 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## COM_A4 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## SAT_1 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## SAT_2 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## SAT_3 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## C_REP1 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## C_REP2 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## C_REP3 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## C_CR1 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## C_CR3 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## C_CR4 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## Im8 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## Im15 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## Im9 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## Im15 Im9
## Im3 NaN NaN
## Im4 NaN NaN
## Im5 NaN NaN
## Im10 NaN NaN
## Im14 NaN NaN
## Im20 NaN NaN
## Im21 NaN NaN
## Im22 NaN NaN
## Im11 NaN NaN
## Im12 NaN NaN
## Im13 NaN NaN
## Im1 NaN NaN
## Im2 NaN NaN
## Im16 NaN NaN
## Im19 NaN NaN
## Im17 NaN NaN
## Im18 NaN NaN
## Im6 NaN NaN
## Im7 NaN NaN
## COM_A1 NaN NaN
## COM_A2 NaN NaN
## COM_A3 NaN NaN
## COM_A4 NaN NaN
## SAT_1 NaN NaN
## SAT_2 NaN NaN
## SAT_3 NaN NaN
## C_REP1 NaN NaN
## C_REP2 NaN NaN
## C_REP3 NaN NaN
## C_CR1 NaN NaN
## C_CR3 NaN NaN
## C_CR4 NaN NaN
## Im8 NaN NaN
## Im15 NaN NaN
## Im9 NaN NaN
# calculate construct reliability (should be above .6)
constrrel <- (t(lambda) %*% ones)^2 / ((t(lambda) %*% ones)^2 + t(theta_lb) %*% ones )
# constrrel
# replace all values satisfying condition with NaN for visibility
constrrel_fail <- constrrel
constrrel_fail[constrrel_fail>.6] <- NaN
constrrel_fail## DECO FOOD ATMOS PRODQUAL CHOICE PROF BRAND FRENCH AFCOM SAT RI COI
## DECO NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## FOOD NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## ATMOS NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## PRODQUAL NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## CHOICE NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## PROF NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## BRAND NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## FRENCH NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## AFCOM NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## SAT NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## RI NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## COI NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## Im8 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## Im15 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## Im9 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## Im8 Im15 Im9
## DECO NaN NaN NaN
## FOOD NaN NaN NaN
## ATMOS NaN NaN NaN
## PRODQUAL NaN NaN NaN
## CHOICE NaN NaN NaN
## PROF NaN NaN NaN
## BRAND NaN NaN NaN
## FRENCH NaN NaN NaN
## AFCOM NaN NaN NaN
## SAT NaN NaN NaN
## RI NaN NaN NaN
## COI NaN NaN NaN
## Im8 NaN NaN NaN
## Im15 NaN NaN NaN
## Im9 NaN NaN NaN
# calculate Average Variance Extracted (should be above .5)
AVE <- (t(lambda) %*% lambda) / (t(lambda) %*% lambda + t(theta_lb) %*% ones )
# avgvar
# replace all values satisfying condition with NaN for visibility
AVE_fail <- AVE
AVE_fail[AVE_fail>.5] <- NaN
AVE_fail## DECO FOOD ATMOS PRODQUAL CHOICE PROF BRAND FRENCH AFCOM SAT RI COI
## DECO NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## FOOD NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## ATMOS NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## PRODQUAL NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## CHOICE NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## PROF NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## BRAND NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## FRENCH NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## AFCOM NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## SAT NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## RI NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## COI NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## Im8 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## Im15 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## Im9 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## Im8 Im15 Im9
## DECO NaN NaN NaN
## FOOD NaN NaN NaN
## ATMOS NaN NaN NaN
## PRODQUAL NaN NaN NaN
## CHOICE NaN NaN NaN
## PROF NaN NaN NaN
## BRAND NaN NaN NaN
## FRENCH NaN NaN NaN
## AFCOM NaN NaN NaN
## SAT NaN NaN NaN
## RI NaN NaN NaN
## COI NaN NaN NaN
## Im8 NaN NaN NaN
## Im15 NaN NaN NaN
## Im9 NaN NaN NaN
# correlations between constructs (factors...) should be lower than .7
psi = inspect(SEM_fit, what="std")$psi
psi_fail <- psi
psi_fail[psi_fail<.7] <- NaN
psi_fail## DECO FOOD ATMOS PRODQU CHOICE PROF BRAND FRENCH AFCOM SAT RI
## DECO 1.000
## FOOD NaN 1.000
## ATMOS NaN NaN 1.000
## PRODQUAL NaN NaN NaN 1.000
## CHOICE NaN NaN NaN NaN 1.000
## PROF NaN NaN NaN NaN NaN 1.000
## BRAND NaN NaN NaN NaN NaN NaN 1.000
## FRENCH NaN NaN NaN NaN NaN NaN NaN 1.000
## AFCOM NaN NaN NaN NaN NaN NaN NaN NaN 0.702
## SAT NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## RI NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN 1.000
## COI NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## Im8 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## Im15 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## Im9 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## COI Im8 Im15 Im9
## DECO
## FOOD
## ATMOS
## PRODQUAL
## CHOICE
## PROF
## BRAND
## FRENCH
## AFCOM
## SAT
## RI
## COI 1.000
## Im8 NaN 1.000
## Im15 NaN NaN 1.000
## Im9 NaN NaN NaN 1.000
# AVE should be higher than squared correlations between constructs
# replace diagonal of psi matrix with AVE values
psi2 <- psi - psi * diag(1,nrow(psi),ncol(psi)) + diag(AVE) * diag(1,nrow(AVE),ncol(AVE))
# create matrix with columns filled with AVE
AVE_full <- AVE
AVE_full[is.na(AVE_full)] <- 0 #replace NAs with 0s
AVE_full <- AVE_full^0 %*% AVE_full # multiply a matrix full of ones with AVE_full to get columns filled with AVE
# substract matrices, replace all values satisfying positive condition (AVE > psi) with NaN
AVEpsi_fail <- AVE_full - psi2
# AVE_full - psi2
AVEpsi_fail[AVEpsi_fail >= 0] <- NaN
AVE_full## DECO FOOD ATMOS PRODQUAL CHOICE PROF BRAND
## DECO 0.7986426 0.8841503 0.7020647 0.6269858 0.880352 0.6554196 0.8357675
## FOOD 0.7986426 0.8841503 0.7020647 0.6269858 0.880352 0.6554196 0.8357675
## ATMOS 0.7986426 0.8841503 0.7020647 0.6269858 0.880352 0.6554196 0.8357675
## PRODQUAL 0.7986426 0.8841503 0.7020647 0.6269858 0.880352 0.6554196 0.8357675
## CHOICE 0.7986426 0.8841503 0.7020647 0.6269858 0.880352 0.6554196 0.8357675
## PROF 0.7986426 0.8841503 0.7020647 0.6269858 0.880352 0.6554196 0.8357675
## BRAND 0.7986426 0.8841503 0.7020647 0.6269858 0.880352 0.6554196 0.8357675
## FRENCH 0.7986426 0.8841503 0.7020647 0.6269858 0.880352 0.6554196 0.8357675
## AFCOM 0.7986426 0.8841503 0.7020647 0.6269858 0.880352 0.6554196 0.8357675
## SAT 0.7986426 0.8841503 0.7020647 0.6269858 0.880352 0.6554196 0.8357675
## RI 0.7986426 0.8841503 0.7020647 0.6269858 0.880352 0.6554196 0.8357675
## COI 0.7986426 0.8841503 0.7020647 0.6269858 0.880352 0.6554196 0.8357675
## Im8 0.7986426 0.8841503 0.7020647 0.6269858 0.880352 0.6554196 0.8357675
## Im15 0.7986426 0.8841503 0.7020647 0.6269858 0.880352 0.6554196 0.8357675
## Im9 0.7986426 0.8841503 0.7020647 0.6269858 0.880352 0.6554196 0.8357675
## FRENCH AFCOM SAT RI COI Im8 Im15 Im9
## DECO 0.7895836 0.667259 0.5996322 0.7084962 0.6811628 1 1 1
## FOOD 0.7895836 0.667259 0.5996322 0.7084962 0.6811628 1 1 1
## ATMOS 0.7895836 0.667259 0.5996322 0.7084962 0.6811628 1 1 1
## PRODQUAL 0.7895836 0.667259 0.5996322 0.7084962 0.6811628 1 1 1
## CHOICE 0.7895836 0.667259 0.5996322 0.7084962 0.6811628 1 1 1
## PROF 0.7895836 0.667259 0.5996322 0.7084962 0.6811628 1 1 1
## BRAND 0.7895836 0.667259 0.5996322 0.7084962 0.6811628 1 1 1
## FRENCH 0.7895836 0.667259 0.5996322 0.7084962 0.6811628 1 1 1
## AFCOM 0.7895836 0.667259 0.5996322 0.7084962 0.6811628 1 1 1
## SAT 0.7895836 0.667259 0.5996322 0.7084962 0.6811628 1 1 1
## RI 0.7895836 0.667259 0.5996322 0.7084962 0.6811628 1 1 1
## COI 0.7895836 0.667259 0.5996322 0.7084962 0.6811628 1 1 1
## Im8 0.7895836 0.667259 0.5996322 0.7084962 0.6811628 1 1 1
## Im15 0.7895836 0.667259 0.5996322 0.7084962 0.6811628 1 1 1
## Im9 0.7895836 0.667259 0.5996322 0.7084962 0.6811628 1 1 1
psi## DECO FOOD ATMOS PRODQU CHOICE PROF BRAND FRENCH AFCOM SAT
## DECO 1.000
## FOOD 0.414 1.000
## ATMOS 0.471 0.299 1.000
## PRODQUAL 0.471 0.448 0.437 1.000
## CHOICE 0.452 0.291 0.462 0.480 1.000
## PROF 0.664 0.507 0.479 0.542 0.607 1.000
## BRAND 0.523 0.325 0.526 0.561 0.516 0.603 1.000
## FRENCH 0.336 0.586 0.333 0.313 0.214 0.368 0.318 1.000
## AFCOM 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.702
## SAT 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.330 0.629
## RI 0.260 0.263 0.380 0.291 0.281 0.364 0.279 0.218 0.000 0.000
## COI 0.041 -0.024 0.209 0.063 0.029 -0.050 0.063 0.003 0.000 0.000
## Im8 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
## Im15 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
## Im9 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
## RI COI Im8 Im15 Im9
## DECO
## FOOD
## ATMOS
## PRODQUAL
## CHOICE
## PROF
## BRAND
## FRENCH
## AFCOM
## SAT
## RI 1.000
## COI 0.074 1.000
## Im8 0.000 0.000 1.000
## Im15 0.000 0.000 0.342 1.000
## Im9 0.000 0.000 0.442 0.397 1.000
AVEpsi_fail## DECO FOOD ATMOS PRODQU CHOICE PROF BRAND FRENCH AFCOM SAT
## DECO .
## FOOD NaN .
## ATMOS NaN NaN .
## PRODQUAL NaN NaN NaN .
## CHOICE NaN NaN NaN NaN .
## PROF NaN NaN NaN NaN NaN .
## BRAND NaN NaN NaN NaN NaN NaN .
## FRENCH NaN NaN NaN NaN NaN NaN NaN .
## AFCOM NaN NaN NaN NaN NaN NaN NaN NaN .
## SAT NaN NaN NaN NaN NaN NaN NaN NaN NaN .
## RI NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## COI NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## Im8 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## Im15 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## Im9 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
## RI COI Im8 Im15 Im9
## DECO
## FOOD
## ATMOS
## PRODQUAL
## CHOICE
## PROF
## BRAND
## FRENCH
## AFCOM
## SAT
## RI .
## COI NaN .
## Im8 NaN NaN .
## Im15 NaN NaN NaN .
## Im9 NaN NaN NaN NaN .
arrange(modificationindices(SEM_fit),-mi)## lhs op rhs mi epc sepc.lv sepc.all sepc.nox
## 1 Im15 ~ CHOICE 182.859 0.498 0.647 0.543 0.543
## 2 Im8 ~ FOOD 165.501 0.651 0.535 0.509 0.509
## 3 Im15 ~ PROF 145.469 0.660 0.613 0.515 0.515
## 4 Im15 ~ SAT 142.423 1.164 0.983 0.825 0.825
## 5 Im8 ~ FRENCH 131.240 0.492 0.480 0.457 0.457
## 6 Im15 ~ BRAND 87.476 0.374 0.451 0.378 0.378
## 7 Im15 ~ PRODQUAL 85.376 0.649 0.463 0.388 0.388
## 8 Im15 ~ DECO 69.835 0.321 0.400 0.336 0.336
## 9 Im15 ~ ATMOS 69.258 0.329 0.413 0.347 0.347
## 10 Im15 ~ AFCOM 68.913 0.686 0.759 0.637 0.637
## 11 ATMOS ~~ AFCOM 66.719 -1.175 -1.011 -1.011 -1.011
## 12 PRODQUAL ~~ AFCOM 66.255 -3.087 -4.673 -4.673 -4.673
## 13 AFCOM =~ C_REP1 63.992 0.168 0.186 0.252 0.252
## 14 FOOD ~ Im8 63.636 0.216 0.263 0.276 0.263
## 15 ATMOS ~ AFCOM 60.988 -1.258 -1.109 -1.109 -1.109
## 16 FRENCH ~ Im8 60.144 0.268 0.275 0.289 0.275
## 17 Im1 ~~ Im2 51.962 97.454 97.454 611.283 611.283
## 18 FRENCH ~ Im9 50.101 0.189 0.194 0.263 0.194
## 19 FRENCH ~ AFCOM 48.545 2.304 2.612 2.612 2.612
## 20 CHOICE ~ Im15 39.126 0.238 0.183 0.219 0.183
## 21 Im10 ~~ Im14 37.411 32.405 32.405 376.274 376.274
## 22 COM_A1 ~~ COM_A2 36.334 0.316 0.316 0.405 0.405
## 23 AFCOM ~~ RI 33.609 0.139 0.257 0.257 0.257
## 24 Im9 ~ BRAND 31.673 0.245 0.295 0.217 0.217
## 25 Im9 ~ FRENCH 31.190 0.304 0.296 0.218 0.218
## 26 AFCOM ~~ COI 31.130 0.422 0.274 0.274 0.274
## 27 Im8 ~ SAT 29.182 0.453 0.383 0.365 0.365
## 28 Im9 ~ PRODQUAL 27.524 0.401 0.286 0.210 0.210
## 29 ATMOS =~ C_REP1 24.770 0.102 0.128 0.173 0.173
## 30 BRAND ~~ SAT 24.417 6.485 8.039 8.039 8.039
## 31 DECO ~~ SAT 24.321 2.606 3.118 3.118 3.118
## 32 Im16 ~~ Im19 24.136 1.186 1.186 2.556 2.556
## 33 PROF ~~ SAT 23.152 -0.480 -0.771 -0.771 -0.771
## 34 Im8 ~ AFCOM 23.017 0.341 0.377 0.360 0.360
## 35 FOOD ~~ SAT 22.611 -1.744 -3.170 -3.170 -3.170
## 36 CHOICE ~~ SAT 21.514 -8.014 -9.211 -9.211 -9.211
## 37 FRENCH ~~ SAT 21.231 -4.090 -6.257 -6.257 -6.257
## 38 CHOICE ~~ AFCOM 20.712 -10.120 -8.413 -8.413 -8.413
## 39 C_REP2 ~~ C_REP3 19.662 0.093 0.093 1.410 1.410
## 40 SAT =~ C_REP1 19.531 0.126 0.107 0.144 0.144
## 41 RI =~ Im22 19.009 -0.376 -0.219 -0.143 -0.143
## 42 BRAND =~ Im13 18.894 0.196 0.236 0.196 0.196
## 43 Im11 ~~ Im13 18.684 -0.182 -0.182 -0.326 -0.326
## 44 SAT ~~ RI 17.728 0.078 0.200 0.200 0.200
## 45 PROF ~ Im15 17.174 0.111 0.120 0.143 0.120
## 46 RI =~ SAT_2 16.948 0.234 0.136 0.138 0.138
## 47 Im8 ~ PROF 16.599 0.192 0.178 0.170 0.170
## 48 PRODQUAL ~ Im9 16.282 0.079 0.111 0.150 0.111
## 49 FOOD ~~ AFCOM 16.106 -1.894 -2.490 -2.490 -2.490
## 50 CHOICE =~ Im20 14.689 -0.154 -0.200 -0.135 -0.135
## 51 SAT =~ COM_A2 14.326 -0.260 -0.220 -0.140 -0.140
## 52 BRAND =~ Im12 14.168 -0.161 -0.194 -0.171 -0.171
## 53 CHOICE ~ SAT 13.130 2.007 1.306 1.306 1.306
## 54 FOOD =~ Im11 12.888 0.218 0.179 0.155 0.155
## 55 CHOICE =~ Im13 12.504 0.129 0.167 0.139 0.139
## 56 COM_A3 ~~ C_REP1 12.474 0.079 0.079 0.188 0.188
## 57 Im21 ~~ C_REP3 11.833 0.054 0.054 0.178 0.178
## 58 Im9 ~ ATMOS 11.772 0.148 0.186 0.136 0.136
## 59 Im9 ~ AFCOM 11.392 0.304 0.336 0.247 0.247
## 60 Im11 ~~ Im12 11.364 0.135 0.135 0.269 0.269
## 61 CHOICE =~ C_REP1 11.252 0.060 0.078 0.105 0.105
## 62 BRAND ~ Im9 11.207 0.099 0.082 0.112 0.082
## 63 RI =~ COM_A1 11.088 0.260 0.152 0.108 0.108
## 64 AFCOM =~ Im11 10.927 0.136 0.150 0.131 0.131
## 65 ATMOS ~ SAT 10.679 -0.764 -0.514 -0.514 -0.514
## 66 FRENCH ~ SAT 10.672 1.428 1.237 1.237 1.237
## 67 Im8 ~ DECO 10.602 0.108 0.134 0.128 0.128
## 68 SAT =~ C_CR4 10.184 0.249 0.210 0.106 0.106
## 69 ATMOS =~ Im12 10.168 -0.113 -0.142 -0.126 -0.126
## 70 Im13 ~~ Im1 10.148 0.067 0.067 0.384 0.384
## 71 PRODQUAL ~ Im15 10.056 0.071 0.099 0.118 0.099
## 72 Im21 ~~ Im22 9.808 -0.190 -0.190 -0.310 -0.310
## 73 PRODQUAL =~ C_CR4 9.798 0.291 0.207 0.104 0.104
## 74 CHOICE =~ Im12 9.543 -0.106 -0.138 -0.122 -0.122
## 75 BRAND =~ Im22 9.380 0.147 0.177 0.116 0.116
## 76 BRAND =~ Im20 9.352 -0.143 -0.172 -0.116 -0.116
## 77 FRENCH =~ C_REP1 9.342 0.072 0.070 0.095 0.095
## 78 Im13 ~~ Im17 9.137 0.068 0.068 0.353 0.353
## 79 COM_A1 ~~ COM_A4 8.747 -0.170 -0.170 -0.211 -0.211
## 80 ATMOS =~ C_CR4 8.454 0.156 0.196 0.099 0.099
## 81 Im10 ~~ Im6 8.438 -0.041 -0.041 -0.174 -0.174
## 82 Im4 ~~ Im17 8.347 -0.044 -0.044 -0.413 -0.413
## 83 DECO ~ SAT 8.162 1.361 0.922 0.922 0.922
## 84 DECO =~ C_REP1 8.000 0.052 0.065 0.088 0.088
## 85 PROF =~ COM_A3 7.907 0.166 0.154 0.097 0.097
## 86 COM_A2 ~~ COM_A3 7.794 -0.167 -0.167 -0.204 -0.204
## 87 PRODQUAL =~ C_CR1 7.757 -0.249 -0.178 -0.091 -0.091
## 88 CHOICE =~ C_REP3 7.675 -0.039 -0.051 -0.091 -0.091
## 89 Im1 ~~ SAT_2 7.648 -0.052 -0.052 -0.319 -0.319
## 90 FOOD =~ Im6 7.597 -0.344 -0.283 -0.235 -0.235
## 91 FOOD =~ Im7 7.597 0.410 0.337 0.279 0.279
## 92 Im10 ~~ Im7 7.537 0.041 0.041 0.359 0.359
## 93 COI =~ C_REP1 7.527 0.038 0.063 0.085 0.085
## 94 Im20 ~~ Im22 7.504 0.206 0.206 0.357 0.357
## 95 DECO =~ Im20 7.348 -0.114 -0.143 -0.096 -0.096
## 96 DECO =~ Im22 7.331 0.117 0.146 0.096 0.096
## 97 SAT =~ COM_A3 7.287 0.190 0.161 0.101 0.101
## 98 SAT ~~ COI 7.250 -0.158 -0.142 -0.142 -0.142
## 99 Im10 ~~ Im16 7.214 0.044 0.044 0.168 0.168
## 100 ATMOS =~ C_REP3 7.085 -0.043 -0.054 -0.096 -0.096
## 101 DECO =~ COM_A3 7.072 0.108 0.135 0.085 0.085
## 102 AFCOM =~ C_CR4 6.939 0.154 0.170 0.086 0.086
## 103 AFCOM =~ Im20 6.866 -0.134 -0.148 -0.099 -0.099
## 104 C_REP1 ~~ C_REP2 6.796 -0.080 -0.080 -0.969 -0.969
## 105 FOOD =~ C_REP1 6.792 0.074 0.060 0.082 0.082
## 106 Im9 ~ DECO 6.779 0.109 0.136 0.100 0.100
## 107 DECO =~ C_CR1 6.728 -0.127 -0.158 -0.081 -0.081
## 108 ATMOS =~ Im11 6.722 0.106 0.133 0.115 0.115
## 109 SAT =~ Im12 6.719 -0.128 -0.108 -0.095 -0.095
## 110 PROF =~ COM_A2 6.718 -0.149 -0.138 -0.088 -0.088
## 111 BRAND =~ Im7 6.517 -0.104 -0.125 -0.103 -0.103
## 112 BRAND =~ Im6 6.517 0.087 0.105 0.087 0.087
## 113 Im3 ~~ Im1 6.441 -0.037 -0.037 -0.297 -0.297
## 114 PROF ~ SAT 6.393 -0.501 -0.456 -0.456 -0.456
## 115 SAT_2 ~~ SAT_3 6.377 -0.096 -0.096 -0.196 -0.196
## 116 Im22 ~~ C_REP3 6.371 -0.040 -0.040 -0.151 -0.151
## 117 COM_A3 ~~ COM_A4 6.348 0.166 0.166 0.196 0.196
## 118 FRENCH =~ Im22 6.233 0.127 0.124 0.081 0.081
## 119 FRENCH =~ C_REP2 6.230 -0.048 -0.047 -0.075 -0.075
## 120 BRAND =~ COM_A3 6.214 0.106 0.128 0.080 0.080
## 121 BRAND =~ Im4 6.167 -0.068 -0.082 -0.061 -0.061
## 122 BRAND =~ C_CR4 6.120 0.131 0.158 0.079 0.079
## 123 Im22 ~~ Im1 5.965 0.062 0.062 0.302 0.302
## 124 PROF =~ C_CR4 5.960 0.176 0.163 0.082 0.082
## 125 PRODQUAL =~ Im5 5.889 0.169 0.120 0.091 0.091
## 126 CHOICE =~ Im5 5.798 0.085 0.111 0.084 0.084
## 127 COM_A1 ~~ SAT_1 5.734 -0.068 -0.068 -0.150 -0.150
## 128 DECO =~ C_CR4 5.702 0.121 0.151 0.076 0.076
## 129 SAT_1 ~~ SAT_3 5.684 0.096 0.096 0.219 0.219
## 130 Im10 ~~ Im13 5.678 -0.034 -0.034 -0.162 -0.162
## 131 Im19 ~~ C_REP1 5.649 -0.038 -0.038 -0.141 -0.141
## 132 Im22 ~~ C_REP2 5.588 -0.034 -0.034 -0.256 -0.256
## 133 RI =~ Im21 5.555 0.194 0.113 0.083 0.083
## 134 DECO =~ Im7 5.478 -0.093 -0.116 -0.096 -0.096
## 135 DECO =~ Im6 5.478 0.078 0.098 0.081 0.081
## 136 Im20 ~~ Im17 5.475 -0.063 -0.063 -0.253 -0.253
## 137 COI =~ SAT_1 5.406 -0.044 -0.074 -0.075 -0.075
## 138 Im9 ~ SAT 5.377 0.246 0.208 0.153 0.153
## 139 COM_A1 ~~ C_REP2 5.374 0.034 0.034 0.214 0.214
## 140 SAT =~ C_CR1 5.309 -0.172 -0.145 -0.074 -0.074
## 141 FRENCH =~ Im20 5.290 -0.115 -0.112 -0.075 -0.075
## 142 BRAND =~ Im5 5.215 0.093 0.112 0.085 0.085
## 143 ATMOS =~ Im5 5.200 0.089 0.112 0.084 0.084
## 144 Im10 ~~ COM_A2 5.195 0.042 0.042 0.142 0.142
## 145 Im13 ~~ Im16 5.110 -0.068 -0.068 -0.142 -0.142
## 146 PRODQUAL =~ Im1 5.074 0.159 0.113 0.085 0.085
## 147 PRODQUAL =~ Im2 5.074 -0.140 -0.100 -0.078 -0.078
## 148 PRODQUAL ~ AFCOM 5.056 -0.492 -0.764 -0.764 -0.764
## 149 Im13 ~~ Im2 5.021 -0.047 -0.047 -0.135 -0.135
## 150 FOOD =~ COM_A3 5.013 0.137 0.113 0.071 0.071
## 151 CHOICE =~ Im22 5.005 0.092 0.120 0.078 0.078
## 152 FOOD ~ AFCOM 4.990 0.539 0.726 0.726 0.726
## 153 PROF =~ Im12 4.951 -0.132 -0.123 -0.108 -0.108
## 154 SAT_3 ~~ C_CR3 4.934 -0.126 -0.126 -0.127 -0.127
## 155 FOOD =~ Im13 4.925 -0.124 -0.102 -0.084 -0.084
## 156 Im3 ~~ COM_A4 4.918 0.057 0.057 0.139 0.139
## 157 Im15 ~ FOOD 4.891 0.130 0.107 0.090 0.090
## 158 Im14 ~~ Im16 4.885 -0.035 -0.035 -0.176 -0.176
## 159 Im1 ~~ SAT_1 4.847 0.041 0.041 0.278 0.278
## 160 Im20 ~~ Im6 4.827 -0.069 -0.069 -0.122 -0.122
## 161 DECO =~ Im18 4.701 0.096 0.120 0.085 0.085
## 162 DECO =~ Im17 4.701 -0.096 -0.120 -0.096 -0.096
## 163 PROF =~ C_REP3 4.690 -0.048 -0.045 -0.079 -0.079
## 164 ATMOS =~ COM_A1 4.664 -0.097 -0.121 -0.086 -0.086
## 165 DECO =~ COM_A2 4.637 -0.085 -0.106 -0.067 -0.067
## 166 Im22 ~~ COM_A1 4.631 -0.085 -0.085 -0.133 -0.133
## 167 Im1 ~~ C_REP3 4.579 -0.022 -0.022 -0.217 -0.217
## 168 AFCOM =~ Im12 4.542 -0.072 -0.080 -0.071 -0.071
## 169 Im20 ~~ Im13 4.512 0.067 0.067 0.136 0.136
## 170 Im4 ~~ Im18 4.472 0.039 0.039 0.158 0.158
## 171 Im13 ~~ SAT_2 4.454 0.049 0.049 0.137 0.137
## 172 Im4 ~~ COM_A3 4.448 0.052 0.052 0.163 0.163
## 173 COI =~ COM_A4 4.402 0.065 0.107 0.063 0.063
## 174 DECO =~ C_REP3 4.388 -0.031 -0.038 -0.068 -0.068
## 175 Im11 ~~ Im6 4.386 -0.066 -0.066 -0.104 -0.104
## 176 BRAND =~ C_CR1 4.338 -0.106 -0.128 -0.065 -0.065
## 177 Im3 ~~ Im4 4.297 0.151 0.151 0.989 0.989
## 178 PROF =~ SAT_2 4.286 0.113 0.105 0.106 0.106
## 179 Im9 ~ FOOD 4.268 0.132 0.109 0.080 0.080
## 180 RI =~ Im16 4.256 -0.174 -0.101 -0.084 -0.084
## 181 Im22 ~~ SAT_3 4.244 -0.077 -0.077 -0.126 -0.126
## 182 AFCOM =~ Im5 4.231 0.082 0.090 0.068 0.068
## 183 Im11 ~~ Im1 4.217 -0.052 -0.052 -0.205 -0.205
## 184 ATMOS =~ C_REP2 4.209 -0.035 -0.044 -0.070 -0.070
## 185 ATMOS =~ Im4 4.208 -0.053 -0.066 -0.049 -0.049
## 186 Im3 ~~ Im5 4.180 -0.067 -0.067 -0.175 -0.175
## 187 FRENCH =~ C_CR4 4.169 0.134 0.131 0.066 0.066
## 188 Im11 ~~ C_REP1 4.127 0.041 0.041 0.100 0.100
## 189 Im20 ~~ Im21 4.109 0.113 0.113 0.168 0.168
## 190 FOOD =~ C_REP2 4.068 -0.047 -0.039 -0.061 -0.061
## 191 FOOD =~ C_CR4 4.061 0.156 0.128 0.065 0.065
## 192 PROF =~ C_REP1 4.060 0.056 0.052 0.071 0.071
## 193 Im7 ~~ C_REP2 3.989 -0.023 -0.023 -0.374 -0.374
## 194 Im14 ~~ Im6 3.978 0.028 0.028 0.155 0.155
## 195 C_REP2 ~~ C_CR4 3.956 -0.042 -0.042 -0.194 -0.194
## 196 BRAND =~ C_REP3 3.918 -0.031 -0.037 -0.066 -0.066
## 197 Im12 ~~ Im7 3.898 0.046 0.046 0.247 0.247
## 198 Im22 ~~ SAT_2 3.894 -0.055 -0.055 -0.132 -0.132
## 199 Im5 ~~ Im6 3.872 -0.060 -0.060 -0.098 -0.098
## 200 COM_A1 ~~ SAT_3 3.837 0.078 0.078 0.104 0.104
## 201 PROF =~ C_CR1 3.832 -0.136 -0.126 -0.064 -0.064
## 202 Im22 ~~ Im11 3.826 0.075 0.075 0.114 0.114
## 203 Im4 ~~ Im6 3.817 0.035 0.035 0.144 0.144
## 204 Im4 ~~ Im11 3.788 -0.043 -0.043 -0.138 -0.138
## 205 Im4 ~~ C_CR1 3.764 -0.059 -0.059 -0.165 -0.165
## 206 BRAND ~~ AFCOM 3.753 3.268 2.931 2.931 2.931
## 207 Im3 ~~ Im2 3.744 0.029 0.029 0.115 0.115
## 208 Im22 ~~ C_REP1 3.729 0.038 0.038 0.115 0.115
## 209 Im14 ~~ Im7 3.715 -0.028 -0.028 -0.328 -0.328
## 210 PROF =~ Im20 3.715 -0.120 -0.111 -0.075 -0.075
## 211 RI =~ Im10 3.676 -0.070 -0.041 -0.046 -0.046
## 212 COM_A1 ~~ C_CR3 3.660 0.113 0.113 0.110 0.110
## 213 Im13 ~~ C_REP2 3.658 0.023 0.023 0.201 0.201
## 214 FOOD =~ Im5 3.653 0.106 0.087 0.066 0.066
## 215 Im20 ~~ COM_A4 3.646 0.084 0.084 0.115 0.115
## 216 Im9 ~ PROF 3.603 0.113 0.105 0.077 0.077
## 217 RI =~ Im5 3.585 0.139 0.081 0.061 0.061
## 218 Im8 ~ ATMOS 3.575 0.064 0.081 0.077 0.077
## 219 DECO ~ AFCOM 3.564 0.671 0.595 0.595 0.595
## 220 AFCOM =~ C_REP3 3.544 -0.032 -0.035 -0.062 -0.062
## 221 PRODQUAL =~ C_REP3 3.501 -0.051 -0.037 -0.065 -0.065
## 222 BRAND =~ SAT_2 3.488 0.059 0.071 0.072 0.072
## 223 Im16 ~~ C_REP3 3.421 -0.028 -0.028 -0.099 -0.099
## 224 COM_A4 ~~ SAT_1 3.420 0.058 0.058 0.123 0.123
## 225 Im22 ~~ SAT_1 3.404 0.050 0.050 0.134 0.134
## 226 Im10 ~~ C_CR1 3.368 0.044 0.044 0.125 0.125
## 227 Im12 ~~ SAT_3 3.362 0.053 0.053 0.114 0.114
## 228 COI =~ C_REP2 3.326 -0.021 -0.034 -0.054 -0.054
## 229 FRENCH =~ COM_A3 3.325 0.097 0.095 0.060 0.060
## 230 SAT =~ Im13 3.313 0.095 0.080 0.066 0.066
## 231 COM_A2 ~~ SAT_1 3.302 -0.054 -0.054 -0.118 -0.118
## 232 Im8 ~ PRODQUAL 3.293 0.110 0.078 0.075 0.075
## 233 Im13 ~~ COM_A2 3.262 -0.062 -0.062 -0.113 -0.113
## 234 Im3 ~~ Im17 3.252 0.028 0.028 0.201 0.201
## 235 PROF =~ SAT_1 3.232 -0.101 -0.094 -0.095 -0.095
## 236 PROF =~ Im13 3.224 0.112 0.104 0.087 0.087
## 237 SAT =~ Im5 3.190 0.097 0.082 0.062 0.062
## 238 Im2 ~~ Im16 3.139 0.043 0.043 0.099 0.099
## 239 Im5 ~~ Im1 3.128 0.043 0.043 0.177 0.177
## 240 Im11 ~~ Im17 3.123 -0.048 -0.048 -0.168 -0.168
## 241 COM_A4 ~~ C_REP1 3.100 0.040 0.040 0.096 0.096
## 242 PROF =~ Im1 3.078 -0.161 -0.150 -0.113 -0.113
## 243 PROF =~ Im2 3.078 0.142 0.132 0.103 0.103
## 244 SAT_1 ~~ C_CR1 3.074 -0.066 -0.066 -0.123 -0.123
## 245 COM_A1 ~~ COM_A3 3.061 -0.093 -0.093 -0.115 -0.115
## 246 C_REP3 ~~ C_CR3 3.058 -0.041 -0.041 -0.097 -0.097
## 247 COI =~ Im19 3.047 0.048 0.080 0.070 0.070
## 248 Im14 ~~ C_CR1 3.041 -0.040 -0.040 -0.150 -0.150
## 249 Im6 ~~ Im7 3.024 14.806 14.806 62.457 62.457
## 250 RI =~ Im7 2.995 -0.133 -0.078 -0.064 -0.064
## 251 Im14 ~~ SAT_2 2.986 0.021 0.021 0.142 0.142
## 252 Im5 ~~ C_REP1 2.956 0.033 0.033 0.084 0.084
## 253 COM_A2 ~~ C_CR1 2.949 0.100 0.100 0.108 0.108
## 254 COM_A2 ~~ SAT_2 2.932 -0.053 -0.053 -0.103 -0.103
## 255 ATMOS =~ COM_A4 2.915 0.086 0.109 0.063 0.063
## 256 Im2 ~~ Im17 2.894 0.030 0.030 0.172 0.172
## 257 Im2 ~~ C_REP2 2.875 -0.016 -0.016 -0.157 -0.157
## 258 Im5 ~~ COM_A2 2.861 0.068 0.068 0.089 0.089
## 259 Im2 ~~ SAT_2 2.861 0.032 0.032 0.098 0.098
## 260 RI =~ Im14 2.860 0.062 0.036 0.042 0.042
## 261 FRENCH =~ Im19 2.859 0.091 0.089 0.078 0.078
## 262 FRENCH =~ Im16 2.859 -0.088 -0.086 -0.071 -0.071
## 263 Im17 ~~ C_REP1 2.857 -0.023 -0.023 -0.163 -0.163
## 264 Im10 ~~ Im12 2.839 0.022 0.022 0.119 0.119
## 265 Im19 ~~ COM_A1 2.835 0.055 0.055 0.104 0.104
## 266 RI =~ Im12 2.825 -0.110 -0.064 -0.057 -0.057
## 267 BRAND ~ SAT 2.813 0.820 0.576 0.576 0.576
## 268 CHOICE =~ Im21 2.809 0.065 0.084 0.062 0.062
## 269 C_REP1 ~~ C_REP3 2.788 -0.028 -0.028 -0.173 -0.173
## 270 PRODQUAL =~ Im4 2.787 -0.077 -0.055 -0.041 -0.041
## 271 Im18 ~~ COM_A1 2.759 -0.056 -0.056 -0.089 -0.089
## 272 Im12 ~~ Im6 2.757 -0.040 -0.040 -0.102 -0.102
## 273 FOOD =~ C_CR1 2.748 -0.124 -0.102 -0.052 -0.052
## 274 Im21 ~~ C_CR3 2.739 -0.094 -0.094 -0.095 -0.095
## 275 C_CR1 ~~ C_CR3 2.730 0.715 0.715 0.587 0.587
## 276 Im18 ~~ Im6 2.728 0.044 0.044 0.086 0.086
## 277 CHOICE =~ Im16 2.711 0.084 0.109 0.090 0.090
## 278 CHOICE =~ Im19 2.711 -0.087 -0.113 -0.099 -0.099
## 279 COI =~ Im11 2.705 0.045 0.074 0.065 0.065
## 280 COM_A4 ~~ SAT_3 2.677 -0.072 -0.072 -0.092 -0.092
## 281 ATMOS =~ C_CR1 2.655 -0.085 -0.106 -0.054 -0.054
## 282 FRENCH =~ Im11 2.653 0.078 0.076 0.066 0.066
## 283 SAT =~ Im17 2.634 0.089 0.075 0.060 0.060
## 284 Im13 ~~ C_REP1 2.622 -0.026 -0.026 -0.094 -0.094
## 285 Im7 ~~ COM_A1 2.603 -0.050 -0.050 -0.170 -0.170
## 286 COI =~ SAT_3 2.592 -0.043 -0.071 -0.064 -0.064
## 287 Im22 ~~ Im12 2.573 -0.047 -0.047 -0.116 -0.116
## 288 Im3 ~~ Im11 2.537 0.036 0.036 0.089 0.089
## 289 COI =~ Im22 2.535 -0.046 -0.076 -0.050 -0.050
## 290 AFCOM =~ SAT_2 2.531 0.060 0.066 0.067 0.067
## 291 Im16 ~~ SAT_1 2.523 -0.042 -0.042 -0.106 -0.106
## 292 PRODQUAL ~~ SAT 2.513 -0.466 -0.975 -0.975 -0.975
## 293 Im3 ~~ COM_A3 2.506 -0.040 -0.040 -0.097 -0.097
## 294 Im2 ~~ C_CR1 2.490 0.056 0.056 0.096 0.096
## 295 COI =~ Im1 2.474 -0.032 -0.052 -0.039 -0.039
## 296 ATMOS =~ Im13 2.458 0.059 0.074 0.061 0.061
## 297 RI =~ Im13 2.458 0.109 0.064 0.053 0.053
## 298 Im20 ~~ COM_A1 2.418 -0.062 -0.062 -0.089 -0.089
## 299 Im14 ~~ Im20 2.404 -0.025 -0.025 -0.125 -0.125
## 300 DECO =~ Im12 2.388 -0.055 -0.069 -0.061 -0.061
## 301 Im10 ~~ Im11 2.384 0.027 0.027 0.088 0.088
## 302 Im4 ~~ Im1 2.350 0.022 0.022 0.229 0.229
## 303 PRODQUAL =~ SAT_1 2.347 -0.085 -0.060 -0.061 -0.061
## 304 Im14 ~~ Im12 2.345 -0.019 -0.019 -0.138 -0.138
## 305 COM_A3 ~~ C_REP2 2.330 -0.024 -0.024 -0.145 -0.145
## 306 Im1 ~~ Im17 2.326 -0.028 -0.028 -0.316 -0.316
## 307 BRAND =~ C_REP1 2.319 0.030 0.036 0.048 0.048
## 308 CHOICE =~ C_CR4 2.304 0.074 0.096 0.048 0.048
## 309 Im14 ~~ COM_A2 2.302 -0.027 -0.027 -0.119 -0.119
## 310 Im3 ~~ Im22 2.298 0.033 0.033 0.104 0.104
## 311 PRODQUAL =~ SAT_2 2.278 0.082 0.058 0.059 0.059
## 312 FRENCH =~ COM_A2 2.273 -0.078 -0.076 -0.048 -0.048
## 313 Im2 ~~ SAT_1 2.266 -0.027 -0.027 -0.094 -0.094
## 314 Im10 ~~ SAT_2 2.263 -0.019 -0.019 -0.097 -0.097
## 315 AFCOM =~ Im2 2.255 0.045 0.050 0.039 0.039
## 316 CHOICE =~ COM_A3 2.237 0.059 0.077 0.048 0.048
## 317 COI =~ COM_A2 2.227 0.043 0.072 0.046 0.046
## 318 Im21 ~~ C_CR4 2.224 0.084 0.084 0.084 0.084
## 319 Im2 ~~ C_REP1 2.211 0.020 0.020 0.077 0.077
## 320 Im12 ~~ Im16 2.208 0.042 0.042 0.097 0.097
## 321 Im4 ~~ COM_A4 2.190 -0.037 -0.037 -0.118 -0.118
## 322 COI =~ Im2 2.190 0.026 0.044 0.034 0.034
## 323 FRENCH =~ C_CR1 2.190 -0.094 -0.092 -0.047 -0.047
## 324 Im14 ~~ C_REP3 2.160 0.010 0.010 0.108 0.108
## 325 DECO ~~ AFCOM 2.143 0.995 0.861 0.861 0.861
## 326 SAT =~ Im20 2.138 -0.088 -0.074 -0.050 -0.050
## 327 Im22 ~~ Im13 2.130 -0.046 -0.046 -0.102 -0.102
## 328 COM_A4 ~~ C_CR4 2.110 0.094 0.094 0.086 0.086
## 329 FOOD =~ Im20 2.103 -0.084 -0.069 -0.046 -0.046
## 330 SAT =~ Im18 2.078 -0.079 -0.067 -0.048 -0.048
## 331 Im11 ~~ Im2 2.073 0.037 0.037 0.073 0.073
## 332 AFCOM =~ Im1 2.045 -0.048 -0.054 -0.040 -0.040
## 333 AFCOM =~ SAT_1 2.024 -0.055 -0.061 -0.061 -0.061
## 334 Im14 ~~ COM_A3 1.986 0.026 0.026 0.110 0.110
## 335 Im17 ~~ COM_A1 1.967 0.039 0.039 0.141 0.141
## 336 FOOD =~ SAT_1 1.956 -0.065 -0.053 -0.054 -0.054
## 337 SAT_2 ~~ C_REP1 1.944 0.020 0.020 0.078 0.078
## 338 FRENCH =~ COM_A1 1.940 -0.068 -0.067 -0.047 -0.047
## 339 Im1 ~~ COM_A4 1.929 -0.041 -0.041 -0.156 -0.156
## 340 PRODQUAL =~ Im17 1.902 0.125 0.089 0.072 0.072
## 341 PRODQUAL =~ Im18 1.902 -0.125 -0.089 -0.064 -0.064
## 342 RI =~ COM_A4 1.900 0.120 0.070 0.041 0.041
## 343 SAT_2 ~~ C_CR3 1.885 0.057 0.057 0.085 0.085
## 344 SAT =~ Im11 1.874 0.080 0.068 0.059 0.059
## 345 Im5 ~~ Im16 1.872 -0.048 -0.048 -0.072 -0.072
## 346 PROF =~ Im22 1.847 0.087 0.081 0.053 0.053
## 347 Im18 ~~ C_REP1 1.839 0.023 0.023 0.070 0.070
## 348 Im11 ~~ C_REP2 1.816 -0.020 -0.020 -0.118 -0.118
## 349 ATMOS ~ Im15 1.808 0.052 0.042 0.050 0.042
## 350 BRAND =~ Im3 1.808 0.036 0.044 0.033 0.033
## 351 Im12 ~~ SAT_1 1.795 -0.028 -0.028 -0.099 -0.099
## 352 C_REP3 ~~ C_CR4 1.794 0.031 0.031 0.073 0.073
## 353 Im20 ~~ C_REP2 1.765 0.019 0.019 0.131 0.131
## 354 Im20 ~~ Im1 1.759 -0.034 -0.034 -0.150 -0.150
## 355 BRAND ~ AFCOM 1.738 0.489 0.449 0.449 0.449
## 356 COM_A3 ~~ C_REP3 1.735 -0.023 -0.023 -0.070 -0.070
## 357 COI =~ SAT_2 1.725 0.026 0.043 0.043 0.043
## 358 Im12 ~~ COM_A2 1.710 0.042 0.042 0.085 0.085
## 359 Im22 ~~ Im2 1.708 -0.033 -0.033 -0.081 -0.081
## 360 BRAND ~ Im15 1.699 0.044 0.037 0.044 0.037
## 361 Im2 ~~ C_REP3 1.699 0.014 0.014 0.067 0.067
## 362 Im4 ~~ Im2 1.691 -0.019 -0.019 -0.098 -0.098
## 363 Im5 ~~ SAT_2 1.684 0.035 0.035 0.071 0.071
## 364 AFCOM =~ Im6 1.679 0.048 0.053 0.044 0.044
## 365 RI =~ Im11 1.675 0.102 0.060 0.052 0.052
## 366 CHOICE =~ Im14 1.669 0.021 0.028 0.032 0.032
## 367 CHOICE =~ Im10 1.669 -0.021 -0.028 -0.031 -0.031
## 368 COM_A3 ~~ SAT_2 1.657 0.041 0.041 0.077 0.077
## 369 Im10 ~~ Im20 1.656 0.022 0.022 0.082 0.082
## 370 PRODQUAL =~ Im19 1.649 0.120 0.085 0.075 0.075
## 371 PRODQUAL =~ Im16 1.648 -0.116 -0.083 -0.068 -0.068
## 372 Im11 ~~ SAT_1 1.648 0.035 0.035 0.076 0.076
## 373 Im20 ~~ COM_A2 1.639 -0.053 -0.053 -0.076 -0.076
## 374 C_REP1 ~~ C_CR3 1.636 0.038 0.038 0.071 0.071
## 375 Im13 ~~ SAT_3 1.633 -0.040 -0.040 -0.076 -0.076
## 376 ATMOS =~ COM_A3 1.627 0.062 0.078 0.049 0.049
## 377 Im13 ~~ Im18 1.608 -0.034 -0.034 -0.076 -0.076
## 378 SAT =~ Im2 1.593 0.062 0.052 0.041 0.041
## 379 Im20 ~~ SAT_2 1.578 0.035 0.035 0.077 0.077
## 380 PRODQUAL =~ Im6 1.553 -0.076 -0.054 -0.045 -0.045
## 381 PRODQUAL =~ Im7 1.553 0.090 0.064 0.053 0.053
## 382 COI =~ Im13 1.548 -0.029 -0.048 -0.040 -0.040
## 383 Im14 ~~ Im2 1.521 0.013 0.013 0.093 0.093
## 384 Im19 ~~ C_REP2 1.518 0.015 0.015 0.136 0.136
## 385 FRENCH ~ Im15 1.500 0.037 0.038 0.046 0.038
## 386 FOOD =~ Im1 1.499 -0.054 -0.044 -0.033 -0.033
## 387 FOOD =~ Im2 1.499 0.048 0.039 0.031 0.031
## 388 FRENCH =~ Im1 1.484 -0.043 -0.042 -0.032 -0.032
## 389 FRENCH =~ Im2 1.484 0.038 0.037 0.029 0.029
## 390 Im21 ~~ SAT_3 1.479 0.046 0.046 0.064 0.064
## 391 SAT_3 ~~ C_REP3 1.471 0.019 0.019 0.062 0.062
## 392 Im7 ~~ COM_A2 1.453 -0.039 -0.039 -0.131 -0.131
## 393 Im20 ~~ SAT_1 1.453 -0.033 -0.033 -0.080 -0.080
## 394 Im10 ~~ C_REP3 1.449 -0.009 -0.009 -0.070 -0.070
## 395 Im22 ~~ Im19 1.448 -0.038 -0.038 -0.088 -0.088
## 396 COM_A1 ~~ SAT_2 1.439 0.035 0.035 0.069 0.069
## 397 Im21 ~~ Im18 1.426 -0.039 -0.039 -0.064 -0.064
## 398 Im3 ~~ Im18 1.403 -0.022 -0.022 -0.070 -0.070
## 399 BRAND =~ COM_A4 1.398 -0.052 -0.063 -0.037 -0.037
## 400 CHOICE =~ COM_A4 1.388 -0.048 -0.062 -0.036 -0.036
## 401 Im2 ~~ Im18 1.384 -0.025 -0.025 -0.063 -0.063
## 402 BRAND =~ SAT_1 1.384 -0.038 -0.046 -0.046 -0.046
## 403 Im5 ~~ Im7 1.347 0.033 0.033 0.115 0.115
## 404 Im2 ~~ COM_A3 1.341 0.033 0.033 0.064 0.064
## 405 COM_A1 ~~ C_REP3 1.341 0.019 0.019 0.060 0.060
## 406 Im7 ~~ SAT_3 1.336 0.034 0.034 0.120 0.120
## 407 Im22 ~~ C_CR1 1.324 -0.061 -0.061 -0.081 -0.081
## 408 Im20 ~~ SAT_3 1.321 0.044 0.044 0.065 0.065
## 409 BRAND =~ COM_A2 1.318 -0.047 -0.057 -0.036 -0.036
## 410 COI =~ Im4 1.314 -0.018 -0.030 -0.022 -0.022
## 411 DECO =~ Im13 1.308 0.043 0.054 0.044 0.044
## 412 Im12 ~~ C_CR3 1.299 0.050 0.050 0.077 0.077
## 413 Im12 ~~ COM_A4 1.299 -0.039 -0.039 -0.076 -0.076
## 414 Im4 ~~ C_CR3 1.288 0.037 0.037 0.092 0.092
## 415 COM_A3 ~~ SAT_3 1.286 -0.049 -0.049 -0.062 -0.062
## 416 SAT_1 ~~ C_CR3 1.274 -0.046 -0.046 -0.076 -0.076
## 417 Im12 ~~ C_REP1 1.266 -0.017 -0.017 -0.068 -0.068
## 418 ATMOS ~~ SAT 1.253 -0.125 -0.148 -0.148 -0.148
## 419 Im12 ~~ Im17 1.253 -0.024 -0.024 -0.136 -0.136
## 420 Im6 ~~ COM_A1 1.240 0.036 0.036 0.059 0.059
## 421 RI =~ Im1 1.236 -0.068 -0.040 -0.030 -0.030
## 422 ATMOS =~ C_CR3 1.228 -0.061 -0.077 -0.037 -0.037
## 423 Im20 ~~ Im19 1.227 0.035 0.035 0.074 0.074
## 424 SAT =~ Im21 1.217 0.065 0.055 0.040 0.040
## 425 PRODQUAL =~ COM_A2 1.207 -0.078 -0.055 -0.035 -0.035
## 426 SAT =~ C_CR3 1.207 -0.087 -0.074 -0.036 -0.036
## 427 ATMOS =~ Im17 1.181 -0.050 -0.063 -0.051 -0.051
## 428 ATMOS =~ Im18 1.181 0.050 0.063 0.045 0.045
## 429 PROF =~ Im7 1.169 -0.067 -0.062 -0.052 -0.052
## 430 PROF =~ Im6 1.169 0.056 0.052 0.044 0.044
## 431 BRAND ~ Im8 1.166 -0.041 -0.034 -0.036 -0.034
## 432 Im19 ~~ SAT_3 1.165 -0.034 -0.034 -0.066 -0.066
## 433 Im14 ~~ Im13 1.160 0.015 0.015 0.093 0.093
## 434 Im13 ~~ C_CR3 1.150 -0.050 -0.050 -0.070 -0.070
## 435 Im6 ~~ C_REP2 1.148 0.013 0.013 0.097 0.097
## 436 Im5 ~~ Im14 1.144 0.017 0.017 0.077 0.077
## 437 Im16 ~~ C_CR4 1.143 -0.057 -0.057 -0.062 -0.062
## 438 Im3 ~~ C_CR1 1.139 0.033 0.033 0.072 0.072
## 439 Im1 ~~ COM_A3 1.137 -0.030 -0.030 -0.116 -0.116
## 440 ATMOS =~ COM_A2 1.135 -0.051 -0.063 -0.040 -0.040
## 441 Im7 ~~ COM_A4 1.132 0.037 0.037 0.119 0.119
## 442 Im16 ~~ C_CR1 1.132 0.054 0.054 0.067 0.067
## 443 PRODQUAL =~ C_REP2 1.125 0.030 0.022 0.034 0.034
## 444 Im21 ~~ Im11 1.123 -0.041 -0.041 -0.054 -0.054
## 445 Im14 ~~ Im17 1.121 0.012 0.012 0.153 0.153
## 446 Im5 ~~ Im2 1.115 -0.026 -0.026 -0.054 -0.054
## 447 SAT =~ Im14 1.111 0.031 0.026 0.030 0.030
## 448 Im12 ~~ SAT_2 1.111 -0.023 -0.023 -0.071 -0.071
## 449 SAT_1 ~~ C_CR4 1.107 0.042 0.042 0.069 0.069
## 450 Im11 ~~ Im7 1.106 0.032 0.032 0.104 0.104
## 451 Im12 ~~ Im13 1.104 0.077 0.077 0.226 0.226
## 452 SAT =~ Im10 1.103 -0.030 -0.026 -0.029 -0.029
## 453 Im17 ~~ C_REP2 1.100 0.011 0.011 0.188 0.188
## 454 Im3 ~~ Im12 1.084 -0.018 -0.018 -0.072 -0.072
## 455 FRENCH ~~ AFCOM 1.083 1.188 1.314 1.314 1.314
## 456 Im17 ~~ COM_A4 1.064 -0.032 -0.032 -0.110 -0.110
## 457 RI =~ COM_A3 1.052 0.087 0.051 0.032 0.032
## 458 PROF =~ Im4 1.046 -0.050 -0.047 -0.034 -0.034
## 459 Im18 ~~ C_REP3 1.035 -0.014 -0.014 -0.052 -0.052
## 460 Im19 ~~ Im7 1.026 0.027 0.027 0.133 0.133
## 461 Im3 ~~ COM_A2 1.026 -0.025 -0.025 -0.062 -0.062
## 462 PRODQUAL =~ COM_A3 1.023 0.073 0.052 0.033 0.033
## 463 Im11 ~~ COM_A3 1.020 0.044 0.044 0.053 0.053
## 464 Im18 ~~ COM_A2 1.018 0.036 0.036 0.056 0.056
## 465 Im22 ~~ Im18 1.017 0.033 0.033 0.062 0.062
## 466 ATMOS ~ Im9 1.016 0.034 0.027 0.037 0.027
## 467 Im10 ~~ Im17 1.010 -0.012 -0.012 -0.114 -0.114
## 468 COM_A2 ~~ COM_A4 1.008 -0.066 -0.066 -0.081 -0.081
## 469 Im22 ~~ Im7 0.994 0.030 0.030 0.123 0.123
## 470 Im12 ~~ C_CR1 0.992 -0.041 -0.041 -0.071 -0.071
## 471 PROF ~ Im8 0.991 0.030 0.033 0.034 0.033
## 472 Im19 ~~ SAT_2 0.986 0.024 0.024 0.068 0.068
## 473 Im1 ~~ Im18 0.978 0.021 0.021 0.104 0.104
## 474 Im3 ~~ SAT_1 0.972 0.016 0.016 0.068 0.068
## 475 AFCOM =~ Im16 0.967 -0.044 -0.049 -0.040 -0.040
## 476 Im12 ~~ COM_A3 0.964 -0.032 -0.032 -0.063 -0.063
## 477 Im11 ~~ SAT_2 0.963 -0.028 -0.028 -0.054 -0.054
## 478 Im6 ~~ SAT_1 0.962 0.022 0.022 0.060 0.060
## 479 Im13 ~~ Im7 0.946 -0.024 -0.024 -0.117 -0.117
## 480 Im18 ~~ Im7 0.944 -0.024 -0.024 -0.101 -0.101
## 481 COM_A2 ~~ SAT_3 0.942 0.040 0.040 0.053 0.053
## 482 SAT_1 ~~ C_REP3 0.932 0.011 0.011 0.058 0.058
## 483 FOOD =~ SAT_2 0.929 0.044 0.036 0.037 0.037
## 484 SAT =~ Im4 0.927 -0.033 -0.028 -0.021 -0.021
## 485 FRENCH =~ Im13 0.926 -0.041 -0.040 -0.033 -0.033
## 486 Im11 ~~ C_CR4 0.924 0.055 0.055 0.051 0.051
## 487 Im19 ~~ Im17 0.923 0.023 0.023 0.121 0.121
## 488 FRENCH =~ Im5 0.920 0.043 0.042 0.032 0.032
## 489 Im1 ~~ C_REP2 0.910 0.009 0.009 0.178 0.178
## 490 Im20 ~~ Im18 0.908 0.031 0.031 0.054 0.054
## 491 FRENCH =~ COM_A4 0.907 0.052 0.051 0.030 0.030
## 492 Im4 ~~ Im22 0.874 -0.020 -0.020 -0.081 -0.081
## 493 ATMOS =~ Im3 0.867 0.024 0.029 0.022 0.022
## 494 PROF =~ Im5 0.861 0.063 0.058 0.044 0.044
## 495 Im7 ~~ C_REP3 0.861 0.011 0.011 0.093 0.093
## 496 Im5 ~~ Im19 0.860 -0.028 -0.028 -0.054 -0.054
## 497 COI =~ Im5 0.858 0.024 0.040 0.030 0.030
## 498 FOOD =~ Im22 0.845 0.054 0.044 0.029 0.029
## 499 Im13 ~~ Im6 0.841 0.024 0.024 0.054 0.054
## 500 Im17 ~~ Im7 0.837 -0.020 -0.020 -0.191 -0.191
## 501 Im12 ~~ C_CR4 0.836 0.039 0.039 0.060 0.060
## 502 Im4 ~~ Im7 0.830 -0.016 -0.016 -0.135 -0.135
## 503 BRAND =~ SAT_3 0.826 -0.036 -0.043 -0.039 -0.039
## 504 FOOD ~ Im9 0.825 0.019 0.023 0.031 0.023
## 505 COM_A4 ~~ SAT_2 0.818 0.029 0.029 0.056 0.056
## 506 Im22 ~~ Im16 0.817 0.033 0.033 0.058 0.058
## 507 Im20 ~~ C_REP3 0.816 -0.014 -0.014 -0.050 -0.050
## 508 CHOICE =~ C_CR1 0.811 -0.042 -0.055 -0.028 -0.028
## 509 Im10 ~~ COM_A3 0.806 -0.017 -0.017 -0.056 -0.056
## 510 COM_A1 ~~ C_REP1 0.804 -0.018 -0.018 -0.046 -0.046
## 511 SAT =~ Im1 0.803 -0.050 -0.042 -0.032 -0.032
## 512 BRAND =~ Im19 0.798 0.051 0.062 0.054 0.054
## 513 BRAND =~ Im16 0.798 -0.049 -0.059 -0.049 -0.049
## 514 Im16 ~~ COM_A4 0.793 -0.037 -0.037 -0.053 -0.053
## 515 Im11 ~~ Im18 0.790 0.029 0.029 0.045 0.045
## 516 Im18 ~~ SAT_1 0.788 -0.021 -0.021 -0.055 -0.055
## 517 Im14 ~~ Im21 0.786 0.015 0.015 0.067 0.067
## 518 Im9 ~ CHOICE 0.783 0.035 0.046 0.034 0.034
## 519 PROF =~ Im17 0.779 0.076 0.071 0.057 0.057
## 520 PROF =~ Im18 0.779 -0.076 -0.071 -0.051 -0.051
## 521 Im7 ~~ SAT_2 0.768 -0.019 -0.019 -0.101 -0.101
## 522 Im4 ~~ Im5 0.764 0.030 0.030 0.103 0.103
## 523 Im10 ~~ COM_A4 0.759 -0.017 -0.017 -0.055 -0.055
## 524 Im11 ~~ COM_A2 0.754 0.037 0.037 0.046 0.046
## 525 FOOD =~ COM_A2 0.752 -0.052 -0.042 -0.027 -0.027
## 526 DECO =~ SAT_2 0.751 0.025 0.031 0.032 0.032
## 527 Im10 ~~ COM_A1 0.740 -0.015 -0.015 -0.052 -0.052
## 528 Im7 ~~ COM_A3 0.732 0.029 0.029 0.093 0.093
## 529 C_CR3 ~~ C_CR4 0.727 -0.331 -0.331 -0.240 -0.240
## 530 CHOICE ~ AFCOM 0.725 0.358 0.305 0.305 0.305
## 531 FRENCH =~ SAT_3 0.721 0.040 0.039 0.035 0.035
## 532 Im7 ~~ C_CR4 0.719 0.037 0.037 0.094 0.094
## 533 CHOICE =~ COM_A2 0.719 -0.033 -0.042 -0.027 -0.027
## 534 Im16 ~~ COM_A3 0.716 0.035 0.035 0.049 0.049
## 535 Im13 ~~ COM_A3 0.708 -0.030 -0.030 -0.052 -0.052
## 536 Im13 ~~ COM_A4 0.705 0.030 0.030 0.054 0.054
## 537 SAT_2 ~~ C_REP2 0.703 0.009 0.009 0.083 0.083
## 538 BRAND =~ Im11 0.700 -0.038 -0.046 -0.040 -0.040
## 539 Im5 ~~ Im11 0.698 0.031 0.031 0.040 0.040
## 540 Im20 ~~ COM_A3 0.689 -0.036 -0.036 -0.049 -0.049
## 541 Im16 ~~ SAT_3 0.689 0.030 0.030 0.046 0.046
## 542 Im12 ~~ Im2 0.681 -0.016 -0.016 -0.052 -0.052
## 543 SAT_2 ~~ C_REP3 0.681 0.010 0.010 0.046 0.046
## 544 Im22 ~~ Im6 0.676 0.025 0.025 0.050 0.050
## 545 ATMOS =~ Im2 0.673 -0.028 -0.035 -0.027 -0.027
## 546 ATMOS =~ Im1 0.673 0.031 0.039 0.029 0.029
## 547 Im10 ~~ C_CR4 0.670 -0.021 -0.021 -0.052 -0.052
## 548 Im1 ~~ C_CR1 0.670 -0.029 -0.029 -0.098 -0.098
## 549 Im22 ~~ Im17 0.669 0.022 0.022 0.097 0.097
## 550 ATMOS =~ SAT_2 0.668 0.025 0.031 0.032 0.032
## 551 Im14 ~~ C_CR4 0.666 0.020 0.020 0.065 0.065
## 552 Im16 ~~ COM_A1 0.665 -0.031 -0.031 -0.045 -0.045
## 553 Im17 ~~ COM_A3 0.664 0.024 0.024 0.085 0.085
## 554 AFCOM =~ Im19 0.663 0.037 0.041 0.036 0.036
## 555 Im10 ~~ C_CR3 0.654 -0.021 -0.021 -0.052 -0.052
## 556 Im5 ~~ Im22 0.651 0.029 0.029 0.047 0.047
## 557 COM_A3 ~~ C_CR3 0.646 0.052 0.052 0.048 0.048
## 558 BRAND =~ Im14 0.641 0.015 0.018 0.021 0.021
## 559 BRAND =~ Im10 0.641 -0.015 -0.018 -0.020 -0.020
## 560 AFCOM =~ Im14 0.628 0.015 0.017 0.020 0.020
## 561 SAT_3 ~~ C_CR1 0.614 0.042 0.042 0.047 0.047
## 562 Im5 ~~ C_CR4 0.609 0.042 0.042 0.042 0.042
## 563 Im19 ~~ SAT_1 0.608 -0.018 -0.018 -0.059 -0.059
## 564 Im20 ~~ Im2 0.603 -0.020 -0.020 -0.044 -0.044
## 565 Im4 ~~ Im16 0.603 0.016 0.016 0.062 0.062
## 566 COI =~ Im12 0.592 0.017 0.028 0.025 0.025
## 567 Im17 ~~ C_REP3 0.584 0.008 0.008 0.074 0.074
## 568 Im19 ~~ Im18 0.583 -0.020 -0.020 -0.047 -0.047
## 569 COM_A4 ~~ C_REP3 0.582 -0.014 -0.014 -0.042 -0.042
## 570 Im14 ~~ C_CR3 0.579 0.019 0.019 0.062 0.062
## 571 RI =~ Im6 0.578 0.049 0.029 0.024 0.024
## 572 Im1 ~~ COM_A1 0.573 0.020 0.020 0.080 0.080
## 573 Im14 ~~ C_REP1 0.570 0.006 0.006 0.055 0.055
## 574 Im14 ~~ Im18 0.569 -0.010 -0.010 -0.057 -0.057
## 575 COI =~ Im16 0.562 -0.021 -0.034 -0.028 -0.028
## 576 Im5 ~~ C_REP2 0.559 -0.010 -0.010 -0.065 -0.065
## 577 Im6 ~~ C_CR4 0.557 -0.034 -0.034 -0.041 -0.041
## 578 FOOD =~ Im4 0.554 -0.027 -0.022 -0.016 -0.016
## 579 Im16 ~~ Im7 0.553 -0.022 -0.022 -0.083 -0.083
## 580 RI =~ Im4 0.552 -0.034 -0.020 -0.015 -0.015
## 581 COI =~ COM_A3 0.549 0.022 0.037 0.023 0.023
## 582 Im21 ~~ COM_A4 0.549 -0.033 -0.033 -0.042 -0.042
## 583 Im13 ~~ Im19 0.549 0.019 0.019 0.053 0.053
## 584 Im14 ~~ SAT_1 0.542 -0.009 -0.009 -0.066 -0.066
## 585 PROF =~ COM_A4 0.539 -0.045 -0.042 -0.024 -0.024
## 586 Im4 ~~ Im12 0.538 0.012 0.012 0.064 0.064
## 587 Im17 ~~ Im6 0.519 0.016 0.016 0.071 0.071
## 588 Im17 ~~ SAT_3 0.519 -0.019 -0.019 -0.072 -0.072
## 589 DECO =~ C_REP2 0.514 -0.011 -0.014 -0.022 -0.022
## 590 FOOD =~ COM_A1 0.511 -0.040 -0.033 -0.023 -0.023
## 591 Im4 ~~ C_REP3 0.508 -0.006 -0.006 -0.052 -0.052
## 592 Im1 ~~ COM_A2 0.501 0.020 0.020 0.078 0.078
## 593 C_CR1 ~~ C_CR4 0.501 -0.275 -0.275 -0.223 -0.223
## 594 PROF =~ COM_A1 0.495 0.038 0.035 0.025 0.025
## 595 Im20 ~~ Im7 0.492 0.021 0.021 0.079 0.079
## 596 Im6 ~~ COM_A3 0.490 -0.025 -0.025 -0.038 -0.038
## 597 CHOICE =~ COM_A1 0.490 0.025 0.033 0.023 0.023
## 598 RI =~ Im17 0.487 0.048 0.028 0.023 0.023
## 599 C_REP2 ~~ C_CR3 0.482 0.015 0.015 0.069 0.069
## 600 Im17 ~~ SAT_2 0.482 0.014 0.014 0.076 0.076
## 601 SAT =~ Im6 0.477 0.035 0.030 0.025 0.025
## 602 Im21 ~~ C_REP1 0.477 -0.014 -0.014 -0.036 -0.036
## 603 PRODQUAL =~ COM_A1 0.476 0.046 0.033 0.023 0.023
## 604 Im11 ~~ COM_A1 0.474 -0.028 -0.028 -0.035 -0.035
## 605 DECO ~ Im15 0.472 0.024 0.019 0.023 0.019
## 606 Im6 ~~ SAT_3 0.469 -0.021 -0.021 -0.036 -0.036
## 607 Im2 ~~ COM_A4 0.468 0.020 0.020 0.039 0.039
## 608 RI =~ Im18 0.466 -0.047 -0.027 -0.020 -0.020
## 609 CHOICE =~ Im3 0.466 -0.016 -0.020 -0.015 -0.015
## 610 Im6 ~~ COM_A2 0.466 0.023 0.023 0.037 0.037
## 611 Im12 ~~ C_REP2 0.462 0.008 0.008 0.074 0.074
## 612 Im18 ~~ C_REP2 0.462 -0.008 -0.008 -0.063 -0.063
## 613 Im10 ~~ Im18 0.462 0.010 0.010 0.041 0.041
## 614 FOOD =~ SAT_3 0.459 0.039 0.032 0.029 0.029
## 615 Im20 ~~ C_REP1 0.456 -0.013 -0.013 -0.037 -0.037
## 616 Im21 ~~ Im17 0.454 0.018 0.018 0.068 0.068
## 617 BRAND =~ Im1 0.454 -0.030 -0.036 -0.027 -0.027
## 618 BRAND =~ Im2 0.454 0.026 0.032 0.025 0.025
## 619 COM_A3 ~~ SAT_1 0.450 0.021 0.021 0.043 0.043
## 620 Im2 ~~ Im7 0.443 0.013 0.013 0.069 0.069
## 621 CHOICE =~ Im11 0.442 -0.026 -0.034 -0.029 -0.029
## 622 Im7 ~~ C_CR1 0.434 -0.028 -0.028 -0.079 -0.079
## 623 AFCOM =~ C_REP2 0.431 -0.010 -0.011 -0.018 -0.018
## 624 Im3 ~~ Im20 0.430 -0.015 -0.015 -0.041 -0.041
## 625 Im5 ~~ Im21 0.427 -0.024 -0.024 -0.033 -0.033
## 626 COM_A1 ~~ C_CR1 0.421 -0.036 -0.036 -0.039 -0.039
## 627 COM_A4 ~~ C_CR3 0.420 -0.043 -0.043 -0.040 -0.040
## 628 PROF =~ Im11 0.413 0.041 0.038 0.033 0.033
## 629 Im10 ~~ Im2 0.411 -0.007 -0.007 -0.038 -0.038
## 630 DECO =~ Im11 0.410 0.026 0.032 0.028 0.028
## 631 Im10 ~~ SAT_3 0.410 0.011 0.011 0.038 0.038
## 632 RI =~ COM_A2 0.409 -0.052 -0.031 -0.019 -0.019
## 633 Im12 ~~ COM_A1 0.408 0.019 0.019 0.040 0.040
## 634 CHOICE =~ C_REP2 0.408 -0.009 -0.012 -0.019 -0.019
## 635 Im21 ~~ SAT_2 0.407 -0.018 -0.018 -0.037 -0.037
## 636 Im3 ~~ Im7 0.407 -0.011 -0.011 -0.074 -0.074
## 637 Im13 ~~ COM_A1 0.405 0.021 0.021 0.038 0.038
## 638 CHOICE =~ SAT_2 0.402 -0.020 -0.026 -0.026 -0.026
## 639 Im3 ~~ Im19 0.398 0.012 0.012 0.044 0.044
## 640 FOOD =~ Im19 0.396 0.045 0.037 0.033 0.033
## 641 FOOD =~ Im16 0.396 -0.044 -0.036 -0.030 -0.030
## 642 CHOICE ~ Im8 0.396 -0.027 -0.021 -0.022 -0.021
## 643 FOOD =~ COM_A4 0.395 -0.040 -0.033 -0.019 -0.019
## 644 Im1 ~~ SAT_3 0.390 0.016 0.016 0.065 0.065
## 645 AFCOM =~ Im10 0.378 -0.012 -0.013 -0.015 -0.015
## 646 SAT =~ Im16 0.375 -0.047 -0.039 -0.033 -0.033
## 647 Im16 ~~ C_REP1 0.375 0.011 0.011 0.033 0.033
## 648 SAT =~ COM_A4 0.375 0.045 0.038 0.022 0.022
## 649 AFCOM =~ Im4 0.364 -0.015 -0.017 -0.012 -0.012
## 650 Im22 ~~ COM_A3 0.361 0.026 0.026 0.038 0.038
## 651 SAT_1 ~~ C_REP2 0.361 -0.006 -0.006 -0.064 -0.064
## 652 Im21 ~~ COM_A1 0.353 0.024 0.024 0.032 0.032
## 653 SAT_2 ~~ C_CR1 0.348 -0.023 -0.023 -0.038 -0.038
## 654 Im6 ~~ C_REP3 0.343 -0.008 -0.008 -0.030 -0.030
## 655 SAT =~ COM_A1 0.342 0.038 0.032 0.023 0.023
## 656 DECO =~ SAT_3 0.330 -0.021 -0.026 -0.024 -0.024
## 657 Im5 ~~ C_CR3 0.325 -0.031 -0.031 -0.031 -0.031
## 658 FOOD ~ Im15 0.324 -0.014 -0.017 -0.020 -0.017
## 659 Im20 ~~ C_CR3 0.323 -0.032 -0.032 -0.035 -0.035
## 660 PROF =~ Im21 0.323 0.034 0.031 0.023 0.023
## 661 COI =~ Im3 0.321 0.009 0.015 0.011 0.011
## 662 Im14 ~~ C_REP2 0.319 -0.004 -0.004 -0.075 -0.075
## 663 ATMOS =~ Im14 0.318 0.010 0.013 0.015 0.015
## 664 ATMOS =~ Im10 0.318 -0.010 -0.013 -0.014 -0.014
## 665 Im17 ~~ C_CR1 0.310 -0.021 -0.021 -0.064 -0.064
## 666 Im11 ~~ COM_A4 0.305 0.025 0.025 0.030 0.030
## 667 Im5 ~~ COM_A4 0.305 -0.024 -0.024 -0.030 -0.030
## 668 Im4 ~~ C_REP2 0.305 0.005 0.005 0.072 0.072
## 669 Im5 ~~ Im17 0.301 0.014 0.014 0.052 0.052
## 670 FOOD =~ Im21 0.300 0.031 0.025 0.018 0.018
## 671 CHOICE =~ Im4 0.295 -0.013 -0.016 -0.012 -0.012
## 672 PRODQUAL =~ Im22 0.295 -0.042 -0.030 -0.020 -0.020
## 673 Im21 ~~ Im1 0.293 0.014 0.014 0.057 0.057
## 674 Im19 ~~ COM_A2 0.293 -0.019 -0.019 -0.035 -0.035
## 675 PRODQUAL =~ Im20 0.286 0.041 0.029 0.019 0.019
## 676 Im4 ~~ COM_A2 0.283 -0.013 -0.013 -0.041 -0.041
## 677 ATMOS =~ SAT_3 0.282 -0.020 -0.025 -0.023 -0.023
## 678 Im21 ~~ COM_A2 0.282 0.022 0.022 0.029 0.029
## 679 Im12 ~~ C_REP3 0.280 -0.006 -0.006 -0.032 -0.032
## 680 Im7 ~~ C_REP1 0.278 0.008 0.008 0.053 0.053
## 681 CHOICE =~ C_CR3 0.274 -0.026 -0.034 -0.016 -0.016
## 682 COM_A4 ~~ C_CR1 0.274 0.032 0.032 0.034 0.034
## 683 Im2 ~~ COM_A1 0.273 -0.014 -0.014 -0.028 -0.028
## 684 CHOICE =~ Im18 0.271 -0.022 -0.028 -0.020 -0.020
## 685 CHOICE =~ Im17 0.271 0.022 0.028 0.023 0.023
## 686 COM_A1 ~~ C_CR4 0.271 -0.030 -0.030 -0.029 -0.029
## 687 FRENCH =~ Im3 0.270 -0.015 -0.014 -0.011 -0.011
## 688 PROF =~ Im3 0.269 0.025 0.023 0.017 0.017
## 689 Im14 ~~ Im22 0.265 0.008 0.008 0.045 0.045
## 690 Im17 ~~ COM_A2 0.264 -0.015 -0.015 -0.054 -0.054
## 691 AFCOM =~ Im7 0.263 -0.023 -0.025 -0.021 -0.021
## 692 RI =~ SAT_1 0.262 -0.028 -0.017 -0.017 -0.017
## 693 Im21 ~~ Im16 0.262 -0.019 -0.019 -0.028 -0.028
## 694 Im16 ~~ C_CR3 0.255 -0.027 -0.027 -0.030 -0.030
## 695 AFCOM =~ Im17 0.254 0.019 0.021 0.017 0.017
## 696 Im6 ~~ C_CR1 0.252 0.022 0.022 0.030 0.030
## 697 Im8 ~ CHOICE 0.251 -0.016 -0.021 -0.020 -0.020
## 698 Im10 ~~ Im21 0.249 -0.009 -0.009 -0.030 -0.030
## 699 Im14 ~~ Im11 0.249 0.008 0.008 0.036 0.036
## 700 AFCOM =~ Im21 0.246 0.024 0.027 0.020 0.020
## 701 Im21 ~~ Im7 0.245 -0.015 -0.015 -0.052 -0.052
## 702 Im1 ~~ Im6 0.239 -0.010 -0.010 -0.051 -0.051
## 703 Im5 ~~ SAT_1 0.239 -0.013 -0.013 -0.029 -0.029
## 704 Im19 ~~ C_CR3 0.237 0.023 0.023 0.033 0.033
## 705 PROF ~ AFCOM 0.233 -0.066 -0.079 -0.079 -0.079
## 706 PRODQUAL =~ COM_A4 0.230 -0.036 -0.026 -0.015 -0.015
## 707 COM_A2 ~~ C_CR4 0.230 -0.029 -0.029 -0.028 -0.028
## 708 DECO =~ Im1 0.230 -0.017 -0.021 -0.016 -0.016
## 709 DECO =~ Im2 0.229 0.015 0.019 0.015 0.015
## 710 Im1 ~~ Im16 0.229 -0.012 -0.012 -0.054 -0.054
## 711 ATMOS =~ Im19 0.229 0.023 0.029 0.025 0.025
## 712 ATMOS =~ Im16 0.229 -0.022 -0.028 -0.023 -0.023
## 713 Im10 ~~ Im22 0.226 -0.008 -0.008 -0.033 -0.033
## 714 COI =~ C_REP3 0.223 -0.005 -0.009 -0.015 -0.015
## 715 COI =~ COM_A1 0.221 0.013 0.022 0.015 0.015
## 716 Im5 ~~ COM_A1 0.220 -0.018 -0.018 -0.024 -0.024
## 717 DECO =~ COM_A1 0.220 -0.017 -0.022 -0.015 -0.015
## 718 AFCOM =~ C_CR3 0.220 0.028 0.031 0.015 0.015
## 719 Im2 ~~ Im19 0.219 -0.010 -0.010 -0.030 -0.030
## 720 COI =~ Im20 0.218 -0.013 -0.022 -0.015 -0.015
## 721 Im19 ~~ C_CR4 0.211 0.021 0.021 0.030 0.030
## 722 PRODQUAL =~ Im3 0.207 0.021 0.015 0.011 0.011
## 723 CHOICE =~ SAT_1 0.207 0.014 0.019 0.019 0.019
## 724 Im21 ~~ Im2 0.205 0.012 0.012 0.024 0.024
## 725 Im16 ~~ SAT_2 0.204 0.012 0.012 0.028 0.028
## 726 DECO =~ SAT_1 0.197 -0.013 -0.016 -0.016 -0.016
## 727 Im5 ~~ SAT_3 0.195 -0.016 -0.016 -0.022 -0.022
## 728 Im3 ~~ C_CR3 0.193 -0.015 -0.015 -0.028 -0.028
## 729 Im3 ~~ C_REP2 0.189 -0.004 -0.004 -0.045 -0.045
## 730 Im17 ~~ C_CR4 0.188 0.017 0.017 0.046 0.046
## 731 Im3 ~~ SAT_2 0.185 -0.007 -0.007 -0.027 -0.027
## 732 FRENCH =~ C_CR3 0.183 -0.029 -0.028 -0.014 -0.014
## 733 Im3 ~~ C_REP3 0.183 0.004 0.004 0.024 0.024
## 734 Im22 ~~ COM_A4 0.180 0.019 0.019 0.028 0.028
## 735 ATMOS =~ SAT_1 0.179 -0.013 -0.016 -0.017 -0.017
## 736 Im14 ~~ Im1 0.179 -0.005 -0.005 -0.064 -0.064
## 737 RI =~ Im19 0.177 -0.035 -0.021 -0.018 -0.018
## 738 Im3 ~~ COM_A1 0.174 -0.010 -0.010 -0.025 -0.025
## 739 PRODQUAL =~ C_REP1 0.171 0.014 0.010 0.014 0.014
## 740 Im14 ~~ SAT_3 0.170 -0.007 -0.007 -0.031 -0.031
## 741 C_REP3 ~~ C_CR1 0.169 0.009 0.009 0.024 0.024
## 742 DECO ~ Im8 0.169 0.016 0.013 0.014 0.013
## 743 Im16 ~~ Im18 0.164 -0.013 -0.013 -0.022 -0.022
## 744 Im1 ~~ C_CR3 0.163 -0.015 -0.015 -0.046 -0.046
## 745 PRODQUAL ~ SAT 0.163 0.119 0.141 0.141 0.141
## 746 Im21 ~~ C_REP2 0.160 -0.006 -0.006 -0.037 -0.037
## 747 Im3 ~~ C_CR4 0.156 -0.013 -0.013 -0.025 -0.025
## 748 Im15 ~ FRENCH 0.152 0.019 0.019 0.016 0.016
## 749 ATMOS ~ Im8 0.151 0.017 0.014 0.014 0.014
## 750 Im1 ~~ Im19 0.151 -0.009 -0.009 -0.051 -0.051
## 751 DECO =~ C_CR3 0.150 0.020 0.025 0.012 0.012
## 752 Im19 ~~ COM_A3 0.150 -0.014 -0.014 -0.025 -0.025
## 753 SAT_3 ~~ C_REP1 0.148 -0.008 -0.008 -0.020 -0.020
## 754 Im2 ~~ C_CR4 0.147 -0.014 -0.014 -0.022 -0.022
## 755 FRENCH =~ Im18 0.144 0.016 0.016 0.011 0.011
## 756 FRENCH =~ Im17 0.144 -0.016 -0.016 -0.013 -0.013
## 757 Im17 ~~ C_CR3 0.144 0.015 0.015 0.041 0.041
## 758 RI =~ C_CR1 0.144 -0.040 -0.024 -0.012 -0.012
## 759 SAT_3 ~~ C_REP2 0.143 -0.005 -0.005 -0.035 -0.035
## 760 SAT =~ C_REP3 0.143 0.009 0.007 0.013 0.013
## 761 PRODQUAL =~ Im14 0.140 0.014 0.010 0.012 0.012
## 762 PRODQUAL =~ Im10 0.140 -0.014 -0.010 -0.011 -0.011
## 763 AFCOM =~ Im18 0.140 -0.014 -0.015 -0.011 -0.011
## 764 Im18 ~~ C_CR1 0.137 0.017 0.017 0.022 0.022
## 765 Im11 ~~ SAT_3 0.136 -0.014 -0.014 -0.019 -0.019
## 766 FRENCH =~ Im21 0.136 -0.018 -0.017 -0.013 -0.013
## 767 FRENCH =~ SAT_2 0.134 -0.014 -0.013 -0.013 -0.013
## 768 DECO ~ Im9 0.132 0.011 0.009 0.012 0.009
## 769 C_REP1 ~~ C_CR4 0.130 0.010 0.010 0.020 0.020
## 770 SAT =~ Im19 0.125 -0.028 -0.023 -0.021 -0.021
## 771 Im4 ~~ SAT_2 0.123 -0.006 -0.006 -0.028 -0.028
## 772 Im18 ~~ SAT_2 0.122 0.008 0.008 0.020 0.020
## 773 RI =~ Im2 0.116 0.019 0.011 0.008 0.008
## 774 Im4 ~~ C_CR4 0.114 0.011 0.011 0.027 0.027
## 775 SAT =~ Im22 0.112 -0.021 -0.017 -0.011 -0.011
## 776 Im10 ~~ Im19 0.112 -0.005 -0.005 -0.024 -0.024
## 777 Im10 ~~ C_REP2 0.112 -0.002 -0.002 -0.035 -0.035
## 778 Im4 ~~ COM_A1 0.112 0.008 0.008 0.025 0.025
## 779 Im11 ~~ C_CR3 0.111 0.019 0.019 0.018 0.018
## 780 DECO =~ Im19 0.109 0.021 0.026 0.023 0.023
## 781 DECO =~ Im16 0.109 -0.020 -0.025 -0.021 -0.021
## 782 Im4 ~~ Im14 0.107 -0.003 -0.003 -0.035 -0.035
## 783 Im17 ~~ SAT_1 0.105 0.006 0.006 0.039 0.039
## 784 COM_A2 ~~ C_REP3 0.104 -0.006 -0.006 -0.017 -0.017
## 785 Im21 ~~ SAT_1 0.104 0.009 0.009 0.020 0.020
## 786 Im21 ~~ Im12 0.104 0.009 0.009 0.020 0.020
## 787 Im18 ~~ C_CR4 0.102 -0.015 -0.015 -0.018 -0.018
## 788 PROF =~ C_CR3 0.101 -0.023 -0.022 -0.011 -0.011
## 789 CHOICE =~ Im6 0.099 -0.009 -0.012 -0.010 -0.010
## 790 CHOICE =~ Im7 0.099 0.011 0.014 0.011 0.011
## 791 Im3 ~~ SAT_3 0.098 -0.007 -0.007 -0.018 -0.018
## 792 Im20 ~~ C_CR4 0.098 -0.018 -0.018 -0.019 -0.019
## 793 SAT =~ C_REP2 0.096 -0.007 -0.006 -0.009 -0.009
## 794 SAT =~ Im7 0.096 -0.019 -0.016 -0.013 -0.013
## 795 Im16 ~~ C_REP2 0.094 -0.004 -0.004 -0.030 -0.030
## 796 PROF =~ SAT_3 0.093 -0.019 -0.018 -0.016 -0.016
## 797 Im5 ~~ Im12 0.092 0.009 0.009 0.018 0.018
## 798 SAT =~ Im3 0.091 0.010 0.009 0.007 0.007
## 799 Im6 ~~ SAT_2 0.089 -0.007 -0.007 -0.017 -0.017
## 800 RI =~ C_CR3 0.089 0.033 0.020 0.009 0.009
## 801 Im20 ~~ Im11 0.085 0.011 0.011 0.016 0.016
## 802 Im2 ~~ Im6 0.085 -0.006 -0.006 -0.015 -0.015
## 803 Im14 ~~ COM_A1 0.084 0.005 0.005 0.022 0.022
## 804 Im21 ~~ C_CR1 0.082 0.015 0.015 0.017 0.017
## 805 Im5 ~~ C_REP3 0.082 0.004 0.004 0.014 0.014
## 806 Im2 ~~ C_CR3 0.081 0.011 0.011 0.016 0.016
## 807 Im5 ~~ Im18 0.081 0.009 0.009 0.014 0.014
## 808 Im4 ~~ Im19 0.078 -0.005 -0.005 -0.025 -0.025
## 809 AFCOM =~ Im22 0.077 -0.015 -0.016 -0.010 -0.010
## 810 FOOD =~ Im17 0.073 0.014 0.011 0.009 0.009
## 811 FOOD =~ Im18 0.073 -0.014 -0.011 -0.008 -0.008
## 812 COI =~ Im6 0.073 -0.006 -0.010 -0.008 -0.008
## 813 COM_A2 ~~ C_CR3 0.072 -0.017 -0.017 -0.016 -0.016
## 814 AFCOM =~ Im3 0.072 -0.007 -0.007 -0.006 -0.006
## 815 Im4 ~~ Im21 0.071 0.006 0.006 0.020 0.020
## 816 Im8 ~ BRAND 0.071 -0.009 -0.011 -0.011 -0.011
## 817 Im7 ~~ C_CR3 0.070 -0.012 -0.012 -0.030 -0.030
## 818 Im11 ~~ C_CR1 0.069 -0.014 -0.014 -0.015 -0.015
## 819 Im4 ~~ SAT_1 0.068 -0.004 -0.004 -0.023 -0.023
## 820 Im18 ~~ C_CR3 0.067 -0.013 -0.013 -0.015 -0.015
## 821 Im11 ~~ Im16 0.067 -0.010 -0.010 -0.014 -0.014
## 822 Im12 ~~ Im18 0.067 -0.006 -0.006 -0.016 -0.016
## 823 Im19 ~~ C_REP3 0.065 0.003 0.003 0.015 0.015
## 824 Im4 ~~ SAT_3 0.062 0.005 0.005 0.018 0.018
## 825 BRAND =~ C_REP2 0.060 0.004 0.005 0.008 0.008
## 826 Im7 ~~ SAT_1 0.059 -0.005 -0.005 -0.031 -0.031
## 827 Im22 ~~ COM_A2 0.057 0.010 0.010 0.015 0.015
## 828 Im20 ~~ Im12 0.053 0.007 0.007 0.015 0.015
## 829 CHOICE =~ SAT_3 0.051 0.009 0.011 0.010 0.010
## 830 SAT_3 ~~ C_CR4 0.051 0.013 0.013 0.013 0.013
## 831 FRENCH =~ SAT_1 0.051 -0.009 -0.008 -0.008 -0.008
## 832 BRAND =~ C_CR3 0.049 -0.012 -0.014 -0.007 -0.007
## 833 Im3 ~~ Im13 0.049 0.004 0.004 0.015 0.015
## 834 Im20 ~~ C_CR1 0.048 0.012 0.012 0.014 0.014
## 835 FOOD =~ C_CR3 0.048 -0.017 -0.014 -0.007 -0.007
## 836 Im2 ~~ SAT_3 0.047 -0.006 -0.006 -0.012 -0.012
## 837 COI =~ Im7 0.046 -0.006 -0.009 -0.008 -0.008
## 838 Im4 ~~ Im20 0.046 -0.005 -0.005 -0.017 -0.017
## 839 CHOICE ~ Im9 0.044 -0.007 -0.005 -0.007 -0.005
## 840 Im3 ~~ Im16 0.044 -0.004 -0.004 -0.013 -0.013
## 841 Im10 ~~ SAT_1 0.043 0.003 0.003 0.015 0.015
## 842 FOOD =~ Im3 0.043 -0.007 -0.006 -0.005 -0.005
## 843 Im11 ~~ C_REP3 0.041 0.003 0.003 0.010 0.010
## 844 PROF ~ Im9 0.040 -0.005 -0.005 -0.007 -0.005
## 845 Im21 ~~ Im13 0.039 -0.006 -0.006 -0.012 -0.012
## 846 SAT_2 ~~ C_CR4 0.037 0.008 0.008 0.012 0.012
## 847 Im1 ~~ C_REP1 0.037 -0.002 -0.002 -0.019 -0.019
## 848 Im19 ~~ Im6 0.036 -0.005 -0.005 -0.012 -0.012
## 849 Im5 ~~ Im10 0.034 -0.003 -0.003 -0.011 -0.011
## 850 Im4 ~~ C_REP1 0.032 -0.002 -0.002 -0.013 -0.013
## 851 Im1 ~~ C_CR4 0.032 -0.007 -0.007 -0.020 -0.020
## 852 Im22 ~~ C_CR3 0.029 0.010 0.010 0.011 0.011
## 853 AFCOM =~ SAT_3 0.029 -0.008 -0.009 -0.008 -0.008
## 854 Im18 ~~ COM_A4 0.028 -0.006 -0.006 -0.010 -0.010
## 855 SAT_1 ~~ SAT_2 0.028 0.009 0.009 0.030 0.030
## 856 Im2 ~~ COM_A2 0.028 -0.005 -0.005 -0.009 -0.009
## 857 COM_A2 ~~ C_REP1 0.028 0.004 0.004 0.009 0.009
## 858 Im6 ~~ C_REP1 0.025 -0.003 -0.003 -0.008 -0.008
## 859 Im20 ~~ Im16 0.024 0.006 0.006 0.009 0.009
## 860 BRAND =~ Im21 0.024 -0.007 -0.008 -0.006 -0.006
## 861 Im5 ~~ C_CR1 0.023 0.008 0.008 0.009 0.009
## 862 Im21 ~~ Im19 0.023 -0.005 -0.005 -0.009 -0.009
## 863 COI =~ Im10 0.023 0.002 0.003 0.003 0.003
## 864 Im19 ~~ C_CR1 0.023 0.007 0.007 0.011 0.011
## 865 Im18 ~~ COM_A3 0.022 0.005 0.005 0.008 0.008
## 866 DECO =~ Im21 0.019 -0.006 -0.007 -0.005 -0.005
## 867 Im3 ~~ Im14 0.019 -0.001 -0.001 -0.012 -0.012
## 868 Im13 ~~ C_CR1 0.019 -0.006 -0.006 -0.009 -0.009
## 869 Im3 ~~ Im21 0.018 -0.003 -0.003 -0.008 -0.008
## 870 Im14 ~~ Im19 0.018 0.002 0.002 0.012 0.012
## 871 RI =~ Im3 0.018 0.006 0.004 0.003 0.003
## 872 Im22 ~~ C_CR4 0.018 0.007 0.007 0.009 0.009
## 873 Im3 ~~ C_REP1 0.017 0.001 0.001 0.007 0.007
## 874 Im13 ~~ SAT_1 0.016 -0.003 -0.003 -0.009 -0.009
## 875 Im3 ~~ Im6 0.016 0.002 0.002 0.007 0.007
## 876 PRODQUAL =~ C_CR3 0.015 -0.012 -0.008 -0.004 -0.004
## 877 Im3 ~~ Im10 0.015 0.001 0.001 0.008 0.008
## 878 AFCOM =~ C_CR1 0.014 0.007 0.007 0.004 0.004
## 879 COI =~ Im14 0.014 -0.001 -0.002 -0.003 -0.003
## 880 PRODQUAL ~ Im8 0.013 0.003 0.004 0.004 0.004
## 881 COM_A2 ~~ C_REP2 0.013 0.002 0.002 0.011 0.011
## 882 PROF =~ Im10 0.012 0.004 0.003 0.004 0.004
## 883 PROF =~ Im14 0.012 -0.004 -0.003 -0.004 -0.004
## 884 C_REP2 ~~ C_CR1 0.012 0.002 0.002 0.011 0.011
## 885 PRODQUAL =~ SAT_3 0.011 0.007 0.005 0.005 0.005
## 886 Im10 ~~ Im1 0.011 -0.001 -0.001 -0.013 -0.013
## 887 Im21 ~~ COM_A3 0.011 -0.004 -0.004 -0.006 -0.006
## 888 Im16 ~~ COM_A2 0.010 0.004 0.004 0.006 0.006
## 889 RI =~ SAT_3 0.010 0.007 0.004 0.004 0.004
## 890 FOOD =~ C_REP3 0.009 -0.002 -0.002 -0.003 -0.003
## 891 RI =~ C_CR4 0.009 0.011 0.006 0.003 0.003
## 892 Im16 ~~ Im6 0.009 -0.003 -0.003 -0.005 -0.005
## 893 PROF ~~ AFCOM 0.009 -0.012 -0.014 -0.014 -0.014
## 894 AFCOM =~ Im13 0.008 -0.003 -0.003 -0.003 -0.003
## 895 Im6 ~~ COM_A4 0.007 -0.003 -0.003 -0.005 -0.005
## 896 Im21 ~~ Im6 0.007 -0.003 -0.003 -0.004 -0.004
## 897 RI =~ Im20 0.007 0.007 0.004 0.003 0.003
## 898 Im4 ~~ Im10 0.006 -0.001 -0.001 -0.007 -0.007
## 899 FRENCH =~ C_REP3 0.006 0.001 0.001 0.003 0.003
## 900 COI =~ Im18 0.006 0.002 0.003 0.002 0.002
## 901 ATMOS =~ Im7 0.005 -0.003 -0.004 -0.003 -0.003
## 902 ATMOS =~ Im6 0.005 0.002 0.003 0.003 0.003
## 903 FOOD ~ SAT 0.003 0.019 0.019 0.019 0.019
## 904 Im18 ~~ SAT_3 0.003 0.002 0.002 0.003 0.003
## 905 Im5 ~~ COM_A3 0.003 0.002 0.002 0.003 0.003
## 906 FOOD =~ Im12 0.003 -0.003 -0.002 -0.002 -0.002
## 907 FRENCH =~ Im10 0.003 0.002 0.002 0.002 0.002
## 908 FRENCH =~ Im14 0.003 -0.002 -0.002 -0.002 -0.002
## 909 Im13 ~~ C_CR4 0.002 0.002 0.002 0.003 0.003
## 910 DECO =~ Im14 0.002 0.001 0.001 0.001 0.001
## 911 DECO =~ Im10 0.002 -0.001 -0.001 -0.001 -0.001
## 912 PRODQUAL =~ Im21 0.001 0.003 0.002 0.001 0.001
## 913 C_REP1 ~~ C_CR1 0.001 -0.001 -0.001 -0.002 -0.002
## 914 Im12 ~~ Im1 0.001 0.001 0.001 0.005 0.005
## 915 Im4 ~~ Im13 0.001 -0.001 -0.001 -0.003 -0.003
## 916 FRENCH =~ Im4 0.001 0.001 0.001 0.001 0.001
## 917 COM_A3 ~~ C_CR4 0.001 -0.002 -0.002 -0.002 -0.002
## 918 COM_A4 ~~ C_REP2 0.001 0.001 0.001 0.003 0.003
## 919 COI =~ Im21 0.001 0.001 0.002 0.001 0.001
## 920 BRAND =~ COM_A1 0.001 -0.001 -0.002 -0.001 -0.001
## 921 FRENCH =~ Im12 0.001 -0.001 -0.001 -0.001 -0.001
## 922 Im5 ~~ Im13 0.001 -0.001 -0.001 -0.002 -0.002
## 923 SAT_1 ~~ C_REP1 0.001 0.000 0.000 -0.002 -0.002
## 924 Im12 ~~ Im19 0.001 0.001 0.001 0.002 0.002
## 925 Im14 ~~ COM_A4 0.001 0.001 0.001 0.002 0.002
## 926 COI =~ Im17 0.001 0.001 0.001 0.001 0.001
## 927 Im1 ~~ Im7 0.001 0.001 0.001 0.005 0.005
## 928 Im11 ~~ Im19 0.001 0.001 0.001 0.001 0.001
## 929 Im13 ~~ C_REP3 0.000 0.000 0.000 -0.001 -0.001
## 930 COM_A3 ~~ C_CR1 0.000 -0.001 -0.001 -0.001 -0.001
## 931 Im5 ~~ Im20 0.000 -0.001 -0.001 -0.001 -0.001
## 932 Im16 ~~ Im17 0.000 0.000 0.000 -0.001 -0.001
## 933 Im19 ~~ COM_A4 0.000 0.000 0.000 0.001 0.001
## 934 PROF =~ C_REP2 0.000 0.000 0.000 0.000 0.000
## 935 Im10 ~~ C_REP1 0.000 0.000 0.000 0.000 0.000
## 936 Im6 ~~ C_CR3 0.000 0.000 0.000 0.000 0.000
## 937 DECO =~ COM_A4 0.000 0.000 0.000 0.000 0.000